In this paper, channel estimation for massive multiple-input multiple-output (MIMO) systems with a large number of transmit antennas at the base station is considered, and a new algorithm for pilot beam pattern design for optimal channel estimation under the assumption of Gauss-Markov channel processes is proposed. The proposed algorithm designs the optimal pilot beam pattern sequentially by exploiting the statistics of the channel, antenna correlation, and temporal correlation. The algorithm provides a sequentially optimal sequence of pilot beam patterns for a given set of system parameters. Numerical results show the effectiveness of the proposed algorithm.