In this paper, a solution to the problem of rest-to-rest three-axis attitude reorientation of a fully actuated rigid body under multiple attitude-constraint zones and angular velocity limits is presented. Based on the unit-quaternion parameterized attitude-constrained zones, a quadratic potential function is developed with a global minimum locating at the desired attitude and high potential closing to the constrained zones, In addition, to limit the magnitude of the angular velocity, another logarithmic potential function is also designed. Using these two potential functions and sliding mode control technique, a nonlinear attitude control law is obtained to guarantee asymptotic convergence of the closed-loop system with consideration of attitude and angular rate constraints, and external disturbances. The effectiveness of the constrained attitude control method is demonstrated through numerical simulation. (C) 2018 Elsevier Ltd. All rights reserved.