Diagonal support is necessary for complex dynamic gait and linear walking of quadruped robots. However, no state estimation method currently supports the corresponding control strategy. In this paper, a state estimation algorithm that fuses inertial measurement units(IMUs) and kinematic constraints is proposed. Firstly, aiming at the pose estimation problem caused by under-constrained kinematics of diagonal support, the kinematic equations are simplified by decomposing the transformation matrix from the body coordinate system to the reference coordinate system, and the analytical formulas of the remaining four pose states are obtained by using the credible pitch and roll measurements of the IMU. Then, based on the differential kinematics of the leg and the pitch and roll angular rates of the IMU, the analytical formulas of the linear velocity and the yaw angular rate are obtained by combining the derivative of pose. Simulation analysis verifies the effectiveness of the proposed algorithm. The experimental results show that the pose estimation values are accurate and drift-free, and the root mean square errors of yaw angular rate and linear velocity are less than 2deg/s and 9mm/s respectively, which outperform existing algorithms and meet the practical control requirements.