With　the　rapidly　changing　states　of　modern　power　systems,　real-time　state　estimation　based　on　phasor　measurement　units　(PMUs)　plays　an　increasingly　important　role　in　energy　management　systems　(EMSs).　However,　due　to　the　complicated　distribution　of　PMU　measurement　errors,　conventional　state　estimation　methods　such　as　the　weighted　least　squares　(WLS)　estimator　suffer　from　the　estimation　bias.　Consequently,　they　do　not　represent　the　least　variance　unbiased　estimators.　To　solve　the　estimation　bias,　a　state　estimation　method　combining　the　PMU　linear　measurement　model　and　the　linear　Bayesian　estimation　theory　is　proposed.　Specifically,　considering　the　prior　information　on　estimated　parameters　and　the　complicated　probability　distribution　of　PMU　measurement　errors,　the　linear　Bayesian　theory　is　applied　to　PMU-based　state　estimation　to　improve　the　performance　of　state　estimation.　To　support　this　method,　the　correlation　between　real　and　imaginary　errors　is　analyzed,　and　the　prior　information　of　estimated　parameters　is　determined　by　the　volatility　of　system　states.　When　the　real　states　of　practical　power　systems　are　unavailable,　performance　indicators　for　state　estimation　are　proposed　based　on　the　estimation　residuals.　The　efficacies　of　the　proposed　estimation　and　evaluation　methods　are　verified　using　IEEE　14　bus　system　and　a　large-scale　power　grid　in　China.