Toward detection of feeble moving infrared spot target, improved Top-Hat morphological filtering operator is presented based on improved genetic algorithms. The optimized improved Top-Hat morphological filter restrains background and noise. And the genetic algorithm is improved with new interval discretization code and adaptive master-slave crossover and mutation operator. The optimized morphological filter based on global search has better filtering and time performance. To different signal to noise ratio (SNR) spot targets, the adaptive threshold is adopted for detection. Experimental results show that the detection probability of complicate images (RSN≈2) can reach more than 70% with false alarm no more than 5%. Compared with fixed Top-Hat filter, the detection probability improves nearly by 10%. Also compared with traditional Top-Hat morphological filter optimized by classical genetic algorithms, the detection probability is improved by 4%.