An atomic clock system based on coherent population trapping (CPT) resonance in Rb-85 is reported, while most past works about the CPT clock are in Rb-87. A new modulation method (full-hyperfine-frequency-splitting modulation) is presented to reduce the effect of light shift to improve the frequency stability of the CPT clock in Rb-85. The experimental results show that the short-term frequency stability of the CPT clock in Rb-85 is in the order of 10(-10)/s and the long-term frequency stability can achieve 1.5 X 10(-11)/80000s, which performs as well as Rb-87 in CPT resonance. This very good frequency stability performance associated with the low-cost and low-power properties of Rb-85 indicates that an atomic clock based on CPT in Rb-85 should be a promising candidate for making the chip scale atomic clock.