In this paper, we propose a novel bit-rate control using information of coded block pattern (CBP) based on statistical moments with respect to the amount of the bits from each macro-block, in an encoding of general video codec such as H.264/AVC and HEVC. Since the proposed bit-rate control is based on the simple computation using the quantization rules in the video codec, it is not necessary for an additional computation, such as a DCT or quantization, to estimate bits for a control of bit-rate. Based on the rate control using the statistical moments, to obtain a more finest video quality, it is necessary to rate control within macro-blocks. For the purpose of a rate control without a discrete cosine transform and quantization, the proposed algorithm employs a mean and a variance of each 4×4 block in a macro-block that is evaluated with the information of motion estimation. Since bit-rates generated by encoding is proportional to a mean and variance, it is possible to raise up or fall down the quantization parameter for a macroblock with a unit value. In addition, since an optimal rate-control is conducted by the Hamiltonian, it is unnecessary to evaluate an accurate bit-rate per 4×4 blocks. As a result, the proposed algorithm can be applied to a single pass encoding, and it can provide enough encoding speed with respect to various applications even requiring real-time without any serious degradation of video quality.