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In this article,two kinds of expandable parallel finite element methods,based on two-grid discretizations,are given to solve the linear elliptic problems. Compared with the classical local and parallel finite element methods,there are two attractive features of the methods shown in this article: 1) a partition of unity is used to generate a series of local and independent subproblems to guarantee the final approximation globally continuous; 2) the computational domain of each local subproblem is contained in a ball with radius of O(H )(H is the coarse mesh parameter),which means methods in this article are more suitable for parallel computing in a large parallel computer system. Some a priori error estimation are obtained and optimal error bounds in both H1-normal and L2-normal are derived. Finally,numerical results are reported to test and verify the feasibility and validity of our methods.