In this paper,a fully discrete scheme based on the L1 approximation in temporal direction for the fractional derivative of order in (0,1) and nonconforming mixed finite element method (MFEM) in spatial direction is established.First,we prove a novel result of the consistency error estimate with order O(h2) of Qrot1 element (see Lemma 2.3).Then,by using the proved character of EQrot1 element,we present the superconvergent estimates for the original variable u in the broken H1-norm and the fluxp→ =▽u in the (L2)2-norm under a weaker regularity of the exact solution.Finally,numerical results are provided to confirm the theoretical analysis.