One part of the saturated absorption spectroscopy on cesium molecules near 780 nm at the absorption band X1Σ+g→B1Πu is obtained. The position of cesium molecular saturated absorption spectroscopy can be determined by 5S1/2(F=2)→5P3/2(F′=2) resonance line of the saturated absorption spectroscopy on 87Rb atom. The five absorption peaks of the saturated absorption spectroscopy are observed. The 780 nm diode laser is stabilized to the “R5” absorption peak. The frequency stability of the laser is better than 1.5 MHz in 800 s. It offers a new method to stabilize the 780 nm diode laser frequency by the saturated absorption peak of cesium molecules. This laser can be used to produce the ultracold ground state cesium molecules,and can be used as the frequency-doubled reference of optical communication range in 1560 nm.