Compliant bipedal robots demonstrate a potential for impact resistance and high energy efficiency through the introduction of compliant elements. However, it also adds to the difficulty of stable control of the robot. To motivate the control strategies of compliant bipedal robots, this work presents an improved control strategy for the stable and fast planar jumping of a compliant one-legged robot designed by the authors, which utilizes the concept of the virtual pendulum. The robot was modeled as an extended spring-loaded inverted pendulum (SLIP) model with non-negligible torso inertia, leg inertia, and leg damping. To enable the robot to jump forward stably, a foot placement method was adopted, where due to the asymmetric feature of the extended SLIP model, a variable time coefficient and an integral term with respect to the forward speed tracking error were introduced to the method to accurately track a given forward speed. An energy-based leg rest length regulation method was used to compensate for the energy dissipation due to leg damping, where an integral term, regarding jumping height tracking error, was introduced to accurately track a given jumping height. Numerical simulations were conducted to validate the effectiveness of the proposed control strategy. Results show that stable and fast jumping of compliant one-legged robots could be achieved, and the desired forward speed and jumping height could also be accurately tracked. In addition to that, using the proposed control strategy, the robust jumping performance of the robot could be observed in the presence of disturbances from state variables or uneven terrain.