Bending behaviors of both a piezoelectric curved bi-morph actuator and a functional gradient piezoelectric curved actuator are studied and compared. The exact solutions of both mechanical and electrical fields of the actuators are obtained based fully on the theory of elasticity. It is found that non-zero normal stresses exist in the gradient piezoelectric curved actuator when the actuator is subjected to an external voltage, which is different from the results obtained in our previous works on the gradient piezoelectric flat actuator. It is also proved that the internal stresses are drastically reduced although the deflection of the gradient curved actuator is quite small. The present analytical solutions are compared with the FEM results and a good agreement is found. (Some figures in this article are in colour only in the electronic version)