The eigenanalysis canceler (EC) method which is suitable for nonhomogeneous clutter can suppress clutter effectively by discarding the eigenvectors of small eigenvalues, which is a well-known subspace-based space-time adaptive processing (STAP) method. However, the computational complexity of conventional EC STAP method is huge due to the eigenvalue decomposition. Moreover, the corresponding performance would be degraded significantly by the subspace leakage phenomenon, since the clutter subspace is not strictly confined to a low-rank subspace any more. Therefore, an improved EC STAP method based on the data-independent clutter subspace estimation is proposed to reduce the computational complexity, where the clutter subspace is rapidly constructed by sampling the prolate spheroidal wave functions (PSWF) non-uniformly. In order to deal with the subspace leakage phenomenon, the proposed EC-PSWF STAP method is modified based on the covariance matrix taper (CMT) to obtain the covariance matrix by re-establishing the noise floor. The corresponding performance of proposed method is evaluated by using the numerical simulation.