DC–DC buck converters are widely adopted to feed power from renewable energy distributed generators into smart grids. Sliding mode control (SMC) schemes enable such converter systems to inject high-accuracy voltage and current into the connected devices or loads, which are of good robustness in dealing with matched disturbances and model uncertainties. However, the chattering phenomenon, caused by the discontinuous control law, leads to large ripples in output voltage and increases switching losses. Moreover, in current sensor failure cases, conventional state feedback control law is not available for higher control performance. In this research paper, a recursive design based universal finite-time observer (UFTO) is applied to reconstruct the current information and lumped disturbances simultaneously, which provides an active disturbance rejection approach. Then, a non-singular sliding mode control based current sensorless finite-time control strategy is developed for the converter system to improve the transmit behaviours, control accuracy, and fault tolerance ability in the presence of various time-varying disturbances. As compared with traditional PID and existing asymptotical current sensorless approaches, both finite-time convergence property of voltage tracking error and active suppression ability against time-varying disturbances are obtained. A rigorous analysis on robustness stability has been provided for the proposed current sensorless finite-time control method. Experimental results are explored to comprehensively illustrate the feasibility and effectiveness of the proposed strategy.