Despite the success and prospects of the robotic catheter system for the cardiovascular access, loss of vision, and haptics have limited its global adoption. A direct implication is the great difficulty posed when trying to eliminate the backlash in catheters during vascular cannulations. As a result, physicians and patients end up been exposed to high radiation for a long period of time. Existing control systems proposed for such interventional robots have not fully consider the hysteretic (backlash) behavior. In this study, a novel robotic catheter system is designed for accessing the human cardiac area through the radial vasculature, while single factor descriptive analysis is employed to characterize the backlash behavior during axial motions of the interventional robot. Based on the descriptive analysis, an adaptive system is proposed for the backlash compensation during the cardiovascular access. The adaptive system consists of a neuro-fuzzy module that predicts a backlash gap based on bounded motion signals, and contact force modulated from a modified error-based force control model. The proposed system is implemented in MATLAB and visual C++. Finally, an in vitro experiment with a human tubular model, shows that the proposed adaptive compensation system can minimize the backlash occurrence during cardiovascular access.