In background subtraction, principal component analysis (PCA) based algorithm has shown remarkable ability to decompose foreground and background in video acquired by static camera. The algorithm via closed form solution of L1-norm Tucker-2 decomposition is one of the real-time background subtraction algorithms. The closed form solution can be obtained from linear combination of video frame vectors and coefficient vector which composed of only +1 and -1. However, since the optimal coefficient vector is unknown, the method cannot help to be a complicated combinatorial optimization problem, when the number of input frame is large. In this paper, to solve this problem, Bayesian optimization (BayesOpt) which is a black-box derivative-free global optimization based background subtraction method is proposed. This method finds the optimal coefficient combination without considering the linear combination of all possible coefficient-combinations, using Bayesian statistical model and Expected Improvement (EI) acquisition function. Here the Bayesian statistical modeling is the method that measures the uncertainty of unsampled coefficient combination points and the EI function is a surrogate function which indicates the next sampling coefficient combination points. The experimental results confirm the efficiency of the proposed method.