As a mature near-space aerial platform, high-altitude scientific balloons exhibit unique advantages in astronomical observations. However, the conventional single-axis attitude pointing control method for balloon-borne gondola platforms, which ignores the roll effect, can no longer fully meet the requirements of emerging space science application scenarios. Therefore, in-depth research on the motion and control characteristics of the pitch/roll channels of the balloon-gondola system is required to improve the overall performance of the attitude control system. Accordingly, the dynamic characteristics of the pitch/roll channels of the balloon-gondola system are modeled using the Lagrangian equation method, and an accurate modal calculation approach is proposed. After linearizing the established dynamic model, its controllability and observability are analyzed, and two control strategies, namely torque damping and active compensation, are put forward. For the torque damping control strategy, a linear quadratic regulator (LQR)-based controller and a Kalman observer are designed, and verification is carried out via Simulink simulation. The proposed dynamic modeling and modal calculation methods for the pitch/roll channels of the balloon-gondola system further reveal the motion characteristics of the coupled system. The proposed control strategies and corresponding simulation results provide an important reference for the design and optimization of attitude control systems for high-altitude scientific balloon gondolas.