This paper describes a novel rate and rate-integrating mode-switchable axisymmetric gyroscope. A precession angle tracking algorithm is developed to enable the gyro to switch automatically between rate and rate-integrating modes at preset rate points through a digital control system within the gyro. We also propose a vibrating amplitude control method for the rate-integrating mode that directly extracts the angular rate output to ensure switching stability. In rate mode, the bias instability and angle random walk of the gyro reach 0.106°/h and 0.011°/√h, respectively. Additionally, an input range of over ±5000°/s is measured in rate-integrating mode. The scale factor nonlinearity reaches approximately 116 ppm over the full-scale range. The control system implements effective steering control of the gyroscope, with a switching delay of 10 ms from rate mode to rate-integrating mode and 100 ms from rate-integrating to rate mode. The proposed system actualizes a new type of gyroscope with high accuracy and a wide input range, which combines the benefits of rate and rate-integrating modes.