This letter focuses on the millimeter wave (mmWave) wideband directional channel estimation for a channel sounding system based on massive multiple-input multiple-output (MIMO). The received signals of the pilot sequence are concatenated into a low-rank third-order tensor. By leveraging the Vandermonde structure of the factor matrices, an algebra-based CANDECOMP/PARAFAC (CP) decomposition is used to reconstruct the factor matrices, from which the channel parameters are estimated by a two-dimensional (2-D) correlation-based search method and refined by the Nelder-Mead simplex (NMS) algorithm. With the Kronecker-structured precoder and combiner, the 2-D search method can be simplified to a 1-D search method. A channel path number estimation method by analyzing the singular values of the expanded signal tensor is also proposed. Simulation results illustrate that the proposed algorithm can obtain high estimation accuracy.