||[[Harrier Attack]]|| 1984 || Amsoft ||No|| Converted by Phantomz<br/>J1B2 = Drop bomb, Pause button = Eject. J1B1 to skip the highscore Table. || [[Media:Harrier Attack.rar | Harrier Attack.rar]]
|-
||[[Harvest Day]]|| 2018 || J.M.L. De Guevara Garcia/A.M. Garcia/D.S. Martinez Pixel Productions || No || Converted by 00WReX || [[Media:Harvest Day.rar | Harvest Day.rar]]
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||[[Harvey Headbanger]]|| 1986 || Firebird ||No|| Converted by Phantomz || [[Media:Harvey Headbanger.rar | Harvey Headbanger.rar]]
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||[[HATE - Hostile All Terrain Encounter]]|| 1989 || Gremlin Graphics Software ||No|| Converted by Phantomz<br/>Pause button = Pause (J1B1 = Resume game) || [[Media:HATE - Hostile All Terrain Encounter.rar | HATE - Hostile All Terrain Encounter.rar]]
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||[[Head Over Heels]]|| 1987 || Ocean Software ||No|| Converted by dragon and Phantomz<br/>Trainer: J1B1 = Yes, J1B2 = No<br/>Redefine controls at first (you will have to use jump and carry together, so leave at least one key defined as both) || [[Media:Head Over Heels.rar | Head Over Heels.rar]]
|-
||[[Heartland]]|| 1986 || Odin Computer Graphics ||No || Converted by Urusergi || [[Media:Heartland.rar | Heartland.rar]]
||[[Hero]]|| 2005 || John Van RYZIN/Flynn ||No|| Converted by Phantomz || [[Media:Hero.rar | Hero.rar]]
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||[[Hero Quest]]|| 1991 || Gremlin Graphics Software||Yes || Converted by dragon and Urusergi (Sorcerer background & part of hardware sprites)<br/>Expanded Plus version requires 128k RAM, standard version available for stock GX4000 || [[Media:Hero Quest.rar | Hero Quest.rar]]
|-
||[[Hexavirus v0]]|| 2019 || [[Kevin_Thacker | Arnoldemu]] ||No|| Converted by [[Kevin_Thacker | Arnoldemu]] || [[Media:Hexavirus v0.rar | Hexavirus v0.rar]]
|-
||[[Hi-Rise]]|| 1986 || Bubble Bus Software || No || Converted by Phantomz<br/>Menu: J1UP/DN/LT/RT+J1B1 = Select start screen, Pause button = Highscore table.<br/>Ingame: J1B2 = Drop Glue, J2B1/B2 = Chasing men slower/faster, J2UP = Quit, J1DN = Suicide, Pause button = Pause (any button to unpause). || [[Media:Hi-Rise.rar | Hi-Rise.rar]]
|-
||[[High Steel]]|| 1989 || Screen 7 ||No || Converted by iXien<br/>J1 D-Pad = up/down/left/right, J1B1 = Pick up / Drop, J1B1+left/right = Throw left/right || [[Media:High Steel.rar | High Steel.rar]]
||[[Hire Hare]]||2016||CNGSoft||No||Converted by iXien||[[Media:Hire Hare.rar|Hire Hare.rar]]
|-
||[[Hit Squad (The)]]|| 1988 || Codemasters Software ||No || Converted by Phantomz<br/>J1B2/J1UP = Jump, Pause button = Pause (J1B1 = Unpause, J2B1= Quit game) || [[Media:Hit Squad (The).rar | Hit Squad (The).rar]]
|-
||[[Hora Bruja]]|| 2011 || ESP Soft ||No|| Converted by McKlain || [[Media:Hora Bruja.rar | Hora Bruja.rar]]
||[[Hunchback]]|| 1985 || Amsoft ||No|| Converted by Phantomz<br/>J1B2 = Instructions || [[Media:Hunchback.rar | Hunchback.rar]]
|-
||[[Hunchback II - Quasimodo's Revenge]]|| 1985 || Ocean Software ||No|| Converted by Phantomz || [[Media:Hunchback II - Quasimodo's Revenge.rar | Hunchback II - Quasimodo's Revenge.rar]]
|-
||[[Hydrofool]]|| 1987 || FTL ||No|| Converted by Phantomz<br/>Select joystick controls before you start the game using the d-pad || [[Media:Hydrofool.rar | Hydrofool.rar]]
|-
||[[Hyper Sports]]|| 1985 || Ocean Software ||No|| Converted by Phantomz || [[Media:Hyper Sports.rar | Hyper Sports.rar]]
|}