This paper describes the effect of a robot cognitive rehabilitation program on cognitive functions for the elderly with mild cognitive impairment, and compares it with traditional cognitive therapy programs. Three experiment groups including cognition therapy group, robot cognitive rehabilitation group, and hybrid group have been sampled and one comparative group has been organized for this research. 32 old people whose ages are between 61 and 88 with mild cognitive impairment participated in the programs with an admission of W care hospital. According to the program results, the cognitive therapy program alone had shown a positive effect on the attention function, and the robot cognitive rehabilitation program alone had a positive effect on the total intelligence and memory function. However, a simultaneous operation with both programs had shown a positive effect on the three intelligence areas such as total, basic, and management quotients as well as attention and memory functions as subsidiary factors. This paper has verified that the proposed robot cognitive rehabilitation program makes a positive effect on a cognitive function and plays a complementary role with traditional cognitive therapy programs.