For　power　system　transient　stability　assessment　(TSA),　the　consequences　of　misclassifications　of　unstable　samples　are　more　serious　than　those　of　stable　samples.　Therefore,　the　cost-sensitive　method　is　introduced　into　TSA.　A　constant　weight　is　set　for　all　unstable　training　samples　by　the　conventional　cost-sensitive　method.　However,　the　fault　severities　of　the　training　samples　are　different.　Thus,　the　impacts　of　the　samples　with　different　fault　severities　on　assessment　rules　are　also　different.　Therefore,　an　improved　cost-sensitive　method　based　on　the　fault　severity　is　proposed.　Firstly,　the　fault　severity　of　each　sample　is　calculated　by　its　fault　clearing　time.　On　this　basis,　different　cost-sensitive　coefficients　are　assigned　to　the　samples　with　different　fault　severities.　The　weights　of　critical　samples　are　larger　than　those　of　non-critical　ones.　Then,　a　stacked　sparse　auto-encoder　model　based　on　the　improved　cost-sensitive　method　is　built　through　modifying　the　loss　function.　Finally,　the　proposed　method　is　tested　in　an　actual　system.　Compared　with　the　traditional　cost-sensitive　method,　the　results　show　that　the　improved　cost-sensitive　method　has　better　performance.　Also,　it　has　the　advantages　of　the　low　false　rate　of　unstable　samples,　high-assessment　accuracy,　and　strong　anti-noise　ability.