Biopsy and brachytherapy for small core breast cancer are always difficult medical problems in the field of cancer treatment. This research mainly develops a magnetic resonance imaging-guided high-precision robotic system for breast puncture treatment. First, a 5-degree-of-freedom tendon-based surgical robotic system is introduced in detail. What follows are the kinematic analysis and dynamical modeling of the robotic system, where a mathematic dynamic model is established using the Lagrange method and a lumped parameter tendon model is used to identify the nonlinear gain of the tendon-sheath transmission system. Based on the dynamical models, an adaptive proportional-integral-derivative controller with friction compensation is proposed for accurate position control. Through simulations using different sinusoidal input signals, we observe that the sinusoidal tracking error at 1/2π Hz is 0.41 mm. Finally, the experiments on tendon-sheath transmission and needle insertion performance are conducted, which show that the insertion precision is 0.68 mm in laboratory environment.