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Motion compensation is the key technology for MMW Costas frequency hopped (FH) radar to realize high range resolution. By defining the waveform entropy for the 1-D range profile of Costas FH radar using an entropy-like function, motion compensation was translated into a one-dimensional optimization problem. A one-dimensional accurate search method based on simulated annealing algorithm was developed and applied to motion compensation of Costas FH radar simulations show that this method is robust, globe and independent of the gradient. High-range-resolution 1-D range profiles of moving targets can be obtained even when the signal to noise ratio (SNR) is nearly 0 dB.