In this paper, we propose a block matching algorithm (BMA) using a genetic algorithm. The genetic algorithm was inspired by an information processing scheme which is used by nature. To use the genetic algorithm in 2D block matching, we encode, based on a quad-tree structure, the phenotype representing a motion vector, i.e., the genotype is represented by four symbol strings. The probability of mutation is differently set for each position in a symbol string. Computer simulation results show that we can have the peak signal to noise ratio (PSNR) of the proposed genetic-based BMA comparable to that of the three step search (TSS) or full search (FS) by varying the number of search points.