The full-information state feedback controller is usually used for regulating the output voltage of converters. Sufficient sensors should be adopted to measure all of the states. However, the extensive use of current sensors not only increases the cost of the overall system, but also affects the reliability. In this paper, the sensorless control problem of DC–DC boost converters is addressed to avoid the need for the current sensor. First, a PI passivity-based control (PI-PBC) is proposed to stabilize this converter. The main feature of this design is that the exponential convergence of the system is guaranteed. Afterward, a generalized parameter estimation-based observer (GPEBO) is presented to estimate the inductor current with the finite-time convergence (FTC). By adding this estimate in the above PI-PBC, a sensorless controller is developed. Thanks to this FTC, the exponential convergence of an overall closed-loop system is ensured. Finally, the simulation and experimental results are given to assess the performance of the proposed controller.