The aim of this paper is to provide a local superconvergence analysis for mixed finite element methods of Poission equation. We shall prove that ifp is smooth enough in a local region % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiqabeqaamaabaabaaGcbaGaeuyQdC1aaS% baaSqaaiaad+gaaeqaaOGaeyOGIWSaeyOGIWSaeuyQdC1aaSbaaSqa% aiaaigdaaeqaaOGaeyOGIWSaeyOGIWSaeuyQdCfaaa!44A3! $$\Omega _o \subset \subset \Omega _1 \subset \subset \Omega $$ and rectangular mesh is imposed on Ω{in1}, then local superconvergence for ∥π{inh}{itu}−{itu}{inh}∥0,2,Ω{in0}, and ∥P{inh}p−p{inh}∥0,2,Ω{in0}, are expected. Thus, by post-processing operators % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiqabeqaamaabaabaaGcbaGabmiuayaaia% aaaa!36D2! $$\tilde P$$ and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiqabeqaamaabaabaaGcbaGafqiWdaNbaG% aaaaa!37BA! $$\tilde \pi $$ , we have obtained the following local superconvergence error estimate: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiqabeqaamaabaabaaGcbaGaaiiFaiaacY% hacaWGWbGaeyOeI0IabmiuayaaiaWaaSbaaSqaaiaadchacaWGObaa% beaakiaacYhacaGG8bGaam4BamaaBaaaleaacaaIXaaabeaakiabfM% 6axnaaBaaaleaacaaIWaaabeaakiaacYhacaGG8bGaey4kaSIaaiiF% aiaacYhacaWG1bGaeyOeI0IafqiWdaNbaGaacaWG1bWaaSbaaSqaai% aadIgaaeqaaOGaaiiFaiaacYhacaWGVbWaaSbaaSqaaiaaigdaaeqa% aOGaeuyQdC1aaSbaaSqaaiaad+gaaeqaaOGaeyizImQaam4yamaadm% aabaGaamiAamaaCaaaleqabaGaam4AaiabgUcaRiaaikdacaGGUaGa% aGynaaaakiaacYhacaGG8bGaamiCaiaacYhacaGG8bGaam4AaiabgU% caRiaaisdadaWgaaWcbaGaaiilaaqabaGccqqHPoWvdaWgaaWcbaGa% aGymaaqabaGccqGHRaWkcaWGObWaaWbaaSqabeaacaWGRbGaey4kaS% IaaGymaiabgUcaRiaadkhacqGHsislcaWGLbaaaOGaaiiFaiaacYha% caWGWbGaaiiFaiaacYhacaaIYaGaey4kaSIaamOCamaaBaaaleaaca% GGSaaabeaakiabfM6axbGaay5waiaaw2faamaaBaaaleaacaGGSaaa% beaaaaa!7C37! $$||p - \tilde P_{ph} ||o_1 \Omega _0 || + ||u - \tilde \pi u_h ||o_1 \Omega _o \leqslant c\left[ {h^{k + 2.5} ||p||k + 4_, \Omega _1 + h^{k + 1 + r - e} ||p||2 + r_, \Omega } \right]_, $$ where 0≤r≤2 andk≥1.