In this paper, we investigated the relative market efficiency of the international market indices in 16 countries, using the approximate entropy (ApEn) method proposed by Pincus (1991), which quantifies a complexity, irregularity and unpredictability in time series. We present our results as follows.First, we found that the ApEn for the random walk is larger than one for non-random walks. Second, we found that the ApEn from the international market indices in 16 countries are shown to be smaller than one from theoretical data generated by the fractional brownian motion (FBM) method with the hurst exponent, H=0.5, which reflects the inefficiency of the market. Therefore, we can not deny an existence of repeated patterns in the empirical time series. Third, the ApEn observed for the various sub-period of the empirical time series have also smaller than one for the random walk.According to the fact that the ApEn are increased, the complexity or irregularity of the present international stock market indices have increased larger than the past. Finally, we found that the ApEn for the some international market indices have the specific behavior which rapidly fell after increases at the market crisis situations.