Conventional　state　estimators,　such　as　the　weighted　least　squares　estimator,　have　been　widely　employed　for　state　estimation　in　power　systems.　However,　these　methods　have　difficulty　addressing　the　leverage　effect　and　rejecting　erroneous　measurements　simultaneously.　In　light　of　these　factors,　this　paper　proposes　a　multi-objective　robust　state　estimator　for　systems　measured　by　phasor　measurement　units　(PMUs)　to　eliminate　the　leverage　effect　and　reject　erroneous　measurements　automatically.　To　reduce　the　computational　complexity,　the　multi-objective　state　estimation　is　solved　by　the　normal　boundary　intersection　method,　and　is　then　transformed　into　a　series　of　single-objective　linear　optimization　problems.　Numerical　simulations　based　on　the　IEEE　14-bus　system　and　an　actual　provincial　760-bus　system　monitored　by　PMUs　are　conducted　to　verify　the　effectiveness　and　robustness　of　the　proposed　estimator　compared　with　two　other　estimators.