Accurate　vehicle　trajectory　prediction　is　critical　for　autonomous　vehicles　and　advanced　driver　assistance　systems　to　make　driving　decisions　and　improve　traffic　safety.　This　paper　proposes　a　novel　Temporal　Multi-task　Mixture　Of　Experts　(TMMOE)　model　for　simultaneously　predicting　the　vehicle　trajectory　and　driving　intention,　considering　interconnections　among　tasks.　As　for　the　methodology,　the　proposed　model　consists　of　three　layers:　a　shared　layer,　an　expert　layer,　and　a　fully　connected　layer.　In　more　detail,　the　first　layer　utilizes　Temporal　Convolutional　Network　(TCN)　to　extract　temporal　features　whereas　the　expert　layer　incorporates　the　gating　mechanism　to　memorize　and　filter　the　temporal　dependence　of　sequences　and,　finally,　the　fully　connected　layer　is　applied　to　integrate　and　export　prediction　results.　Furthermore,　the　homoscedastic　uncertainty　algorithm　is　used　to　construct　the　multi-task　loss　function.　The　open　data　source　CitySim　dataset　is　chosen　to　validate　the　performance　of　the　proposed　TMMOE　model;　moreover,　a　novel　lane　line　reconstruction　method　is　introduced　to　mitigate　measurement　errors　of　the　dataset.　Two-part　information,　including　the　history　of　the　vehicle＇s　trajectory　and　the　interaction　indicators,　are　employed　as　the　input　variables.　The　result　indicates　that　the　TMMOE　algorithm　exhibits　superior　performance　when　compared　to　the　other　five　models,　including　Long　Short-Term　Memory　(LSTM)　Network,　Convolutional　Neural　Network　(CNN),　CNN-LSTM,　TCN,　and　Gate　Recurrent　Unit　(GRU),　while　considering　varying　input　sequence　lengths　are　3　s,　6　s,　and　9　s　respectively.　Finally,　the　sensitivity　analysis　demonstrates　that　considering　driving　intentions　in　vehicle　trajectory　prediction　can　significantly　enhance　the　prediction　accuracy　of　vehicle　trajectories.