Although Cu and hydroxyapatite (Cu-HAp) composite coatings can effectively improve the comfort and friction resistance of medical surgical titanium alloy implants, however, different jet electrodeposition parameters and surface roughness of coatings may exert different impacts on the friction properties of titanium alloy Cu-HAp coatings. Therefore, quantitative research about the influence of these factors on friction characteristics is of great significance. The Cu-HAp coatings are prepared on the Ti6AI7Nb titanium alloy substrate, and surface roughness and average friction coefficient of coatings are measured. Besides, the most significant factor affecting the average friction coefficient of coatings is determined by the gray correlation theory. According to the single-factor analysis method, the effects of surface roughness, current density, and number of deposition layers on the average friction coefficient are examined, and a multiple regression model regarding to the three influence factors for average friction coefficient is established. Finally, based on the particle swarm optimization algorithm, the optimal parameters are obtained. The results demonstrate that the average friction coefficient has the highest correlation with surface roughness, followed by current density and number of deposition layers, and the gray correlation coefficients are 0.84, 0.77 and 0.76, respectively. The accuracy of the model is 92.8 %. According to the model, the average friction coefficient is positively correlated with surface roughness and deposition layers, and negatively correlated with current density. The optimal parameters are Ra = 3.681 εm, J = 57.51 A(dm)−2, n = 2524, corresponding to fm = 0.014.