Seismic　inversion　is　a　process　to　obtain　the　spatial　structure　and　physical　properties　of　underground　rock　formations　by　using　surface　acquired　seismic　data,　constrained　by　known　geological　laws,　drilling　and　logging　data.　The　principle　of　seismic　inversion　based　on　deep　learning　is　to　learn　the　mapping　between　seismic　data　and　rock　properties　by　training　a　neural　network　using　logging　data　as　labels.　However,　due　to　high　cost,　the　number　of　logging　curves　are　often　limited,　leading　to　a　trained　model　with　poor　generalization.　Multi-task　learning　(MTL)　provides　an　effective　way　to　mitigate　this　problem.　Learning　multiple　related　tasks　at　the　same　time　can　improve　the　generalization　ability　of　the　model,　thereby　improving　the　performance　of　the　main　task　on　the　same　amount　of　labeled　data.　However,　the　performance　of　multi-task　learning　is　highly　dependent　on　the　relative　weights　for　the　loss　of　each　task,　and　manual　tuning　of　the　weights　is　often　time-consuming　and　laborious.　In　this　paper,　a　method　based　on　homoscedastic　uncertainty　of　the　Bayesian　model　is　used　to　balance　the　weights　of　the　loss　function　for　multiple　tasks,　and　a　Fully　convolutional　residual　network　(FCRN)　is　used　to　achieve　seismic　impedance　inversion　and　seismic　data　reconstruction　simultaneously.　The　test　results　on　the　synthetic　dataset　of　Marmousi2　model　show　that　the　proposed　method　can　automatically　determine　the　approximate　optimal　weight　of　the　two　tasks,　and　predicts　impedance　with　higher　accuracy　than　single-task　FCRN　model.　©　2022　IEEE.