In this paper, adaptive pilot beam sequence design for channel estimation in large millimeter-wave (mmWave) MIMO systems is considered. By exploiting the sparsity of mmWave MIMO channels with the virtual channel representation and imposing a Markovian random walk assumption on the physical movement of the line-of-sight (LOS) and reflection clusters, it is shown that the sparse channel estimation problem in large mmWave MIMO systems reduces to a sequential detection problem that finds the locations and values of the non-zero-valued bins in a two-dimensional rectangular grid, and the optimal adaptive pilot design problem can be cast into the framework of a partially observable Markov decision process (POMDP). Under the POMDP framework, an optimal adaptive pilot beam sequence design method is obtained to maximize the accumulated transmission data rate for a given period of time. Numerical results are provided to validate our pilot signal design method and they show that the proposed method yields good performance.