Based on an artificial neural network, the training function fitting of the laser-cutted Ni-based alloy samples is conducted. With the current, pulse width, cutting speed and defocusing amount as the input vectors and the comprehensive score of the slag width, kerf width, and cutting integrity as the output vector, the hidden layer node with the minimum error is found. Based on this model, the laser cutting quality is predicted. The maximum error is 7.66% and the minimum error is -0.32%. With the comprehensive score as the fitness value of the genetic algorithm, 50 species within the range of the practical process parameters are randomly selected as the initial optimal group. The treatments such as crossover, mutation and iteration are then made and the optimal fitness value and its corresponding process parameters are searched. The optimal fitness value which is predicted theoretically is 98.41, but the actual value is 89.53, and the error is 9.03%. The quality of this verification sample is obviously higher than those of 25 experimental samples. The average slag width is 81.5 μm and the kerf width is 164 μm.