Consider L2-projection uh of u to n-degree finite element space on one-dimensional uniform grids. Two different classes of the orthogonal expansion in an element for constructing a superclose to function uh are proposed and then superconvergence for both uh and Duh are proved. When n is odd and no boundary conditions are prescribed, then uh is of superconvergence at n+1 order Gauss points Gn+1 in each element. When n is even and function values on the boundary are prescribed, then uh is of superconvergence at n+1 order points Zn+1 in each element. If the other boundary conditions are given, then the conclusions are valid in all elements that its distance from the boundary≥ch|lnh|. The above conclusions are also valid. for n-dergree rectangular element Q1 （n）.
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