We consider channel estimation for massive multiple-input multiple-output (MIMO) systems operating in frequency division duplexing (FDD) mode. By exploiting the sparsity of significant propagation paths in massive MIMO channels, we develop a compressed sensing (CS) based channel estimator that can reduce the pilot overhead as compared with the conventional least squares (LS) and minimum mean square error (MMSE) estimators. The proposed scheme is based on the oblique matching pursuit (ObMP), an extension of the orthogonal matching pursuit (OMP), that can exploit prior information about the sparse signal vector. Given the channel covariance matrix, we obtain the incidence probability that each quantized angle coincides with the angle-of-departure (AoD) and use the incidence probability for deriving the oblique operator of the proposed scheme. The pilot sequence is designed to minimize the MSE of the oracle estimator. The simulation results demonstrate the advantage of the proposed scheme over various existing methods including the LS, MMSE and OMP estimators.