Satellite attitude control to perform designed tasks such as Earth observation, communication and navigation usually requires high accuracy and efficiency. Common control algorithms like Proportional- Derivative (PD) control or Linear Quadratic Regulator (LQR) control do not inherently account for model uncertainties and disturbances in a satellite. This paper proposes a modified sliding mode control (SMC) algorithm to accommodate changes in the satellite's moment of inertia and environmental disturbance torques such as gravitational torques, magnetic field induced torques, etc. The satellite model is considered a rigid rectangular block, including 4 reaction wheels installed in a pyramid configuration for attitude control. The SMC controller is designed based on the quaternion representation of the satellite dynamics model, which is then used to control the satellite model accounting for inertia moment uncertainty and torque disturbances. The numerical simulation is conducted using Matlab/Simulink software to confirm the effectiveness of the proposed SMC algorithm across various criteria such as settling time, and average actuator power consumption in comparison with the PD and LQR controllers.