The discovery of the momentum space crystal based on the alkaline-earth atom Sr-88 in narrow-line cooling has paved the way to explore this novel physical phenomenon in other cold atom systems. In this paper, a momentum space crystal based on the fermions Sr-87 in narrow-line cooling of transition S-1(0)-P-3(1) is demonstrated. We theoretically analyze and compare the formation principle of the narrow-line with that of broad-line cooling, and achieve the momentum space crystal in experiment. Beyond that we present a series of numerical calculations of those important parameters which influence the distribution and size of the momentum space crystal. Correspondingly, we vary the values of these parameters in experiment to observe the momentum space crystal evolution and distribution. The experimental results are in conformity with the results of the theoretically numerical calculations. These results and analyses provide a detailed supplementary study on the formation and evolution of momentum space crystal. In addition, this work could also give a guideline on atomic manipulation by narrow-line cooling.