Intelligent reflecting surface (IRS) consists of a large number of low-cost passive reflective elements, which can assist millimeter wave communications to solve the problems of weak penetration and short propagation distance. However, it is challenging to obtain channel state information (CSI) in IRS-aided millimeter wave communication systems. To solve this challenge, this paper proposes a regular alternating least squares (RALS) algorithm based on the canonical/parallel factor (CP) decomposition. Compared with the traditional alternate least squares (ALS) algorithm, the proposed RALS algorithm has better convergence performance, thus solving the problem of divergence or slow convergence of the conventional ALS algorithm. Besides, in order to improve the accuracy of the channel estimation, the convex optimization theory is invoked to devise the regularization parameters, and a regularization parameter selection scheme is developed to ensure that the proposed algorithm obtains the optimal solution. The simulation results verify the theoretical analysis and prove the superiority of the proposed RALS algorithm in terms of estimation error performance.