Petroleum　reservoirs　are　often　influenced　by　various　flow　behaviours　including　the　mixture　of　gas,　water　and　oil.　The　gas　relative　permeability　is　used　to　estimate　how　much　of　the　gas　in　the　reservoir　is　producible　at　a　given　water　saturation　level.　Therefore,　the　gas　relative　permeability　is　a　significant　parameter　to　characterize　the　behaviour　of　petroleum　reservoirs.　However,　the　measurement　of　gas　relative　permeability　by　traditional　methods　tends　to　be　comparatively　expensive　and　time-consuming.　In　the　recent　years,　the　machine　learning　techniques　provided　new　alternatives　for　predicting　the　gas　relative　permeability.　For　this　purpose,　five　new　methods　were　proposed　based　on　kernel　extreme　learning　machine　(KELM)　technique.　Five　meta-heuristic　algorithms　were　adopted　to　tune　the　model　hyper-parameters　of　KELMs,　i.e.,　butterfly　optimization　algorithm　(BOA),　tunicate　swarm　algorithm　(TSA),　Multi-verse　optimizer　(MVO),　Golden　jackal　optimization　(GJO)　and　Harris　hawk＇s　optimization　(HHO).　Five-fold　cross　validation　was　used　to　increase　the　model　generalization.　An　extensive　dataset　from　the　experiments　which　contain　1024　data　were　taken　to　develop　models.　Four　classical　statistical　indicators　were　used　to　measure　the　model　performance,　i.e.,　root　mean　squared　error　(RMSE),　coefficient　of　determination　(R2),　variance　accounted　for　(VAF)　and　mean　absolute　error　(MAE).　In　addition,　two　comprehensive　manners,　overall　evaluation　index　(GI)　and　Taylor　Diagram,　were　evaluated　to　provide　overall　model　assessments.　Proposed　hybrid　KELM　models　performed　better　than　several　other　machine　learning　techniques.　BOA-KELM　model　with　swarm　size　150　generated　the　best　generalization　for　the　testing　set　and　could　be　recommended　to　predict　the　gas　relative　permeability　with　the　same　inputs　used　in　this　study.　The　detailed　performance　of　BOA-KELM　includes:　training　set　(GI:0.1736;　R2:　0.9902;　RMSE:　0.7477;　VAF:　99.0218;　MAE:　10.6636),　testing　set　(GI:0.4164;　R2:　0.9789;　RMSE:　0.5314;　VAF:　97.8917;　MAE:　4.1706).　The　mutual　information　technique　was　employed　to　examine　the　influence　of　influential　factors　to　the　model　interpretation　and　it　can　be　found　that　the　gas　saturation　had　a　larger　influence　on　the　hybrid　KELM　models.　When　it　was　used　as　an　individual　input,　the　overall　prediction　decreased　but　acceptable　prediction　performance　still　can　be　obtained　by　hybrid　KELM　models.　In　the　case　of　the　gas　saturation　to　be　the　only　input,　the　best　testing　R2　(0.94)　could　be　generated　by　MVO-KELM　which　is　higher　than　the　R2　from　the　empirical　method　named　Corey-Brooks　model　and　several　other　machine　learning　techniques.　The　main　novelty　of　this　study　is　that　five　new　machine　learning　methods　were　proposed　to　predict　the　gas　relative　permeability　and　performed　better　than　other　empirical　or　machine　learning　techniques.　Five　new　methods　based　on　KELM　were　proposed　to　predict　gas　relative　permeability　in　reservoir.Meta-heuristic　algorithms　were　used　to　tune　the　hyper-parameters　in　KELM.BOA-KELM　model　with　swarm　size　150　brought　the　best　generalization　ability.Hybrid　KELM　models　performed　better　than　other　classical　and　machine　learning　model　for　multi-inputs.Mutual　information　was　used　to　explore　the　interpretation　of　inputs.