To improve the on-line laser-ranging performance of light detection and ranging (LiDAR), the run time and resource consumption of the commonly used Gauss-Newton method need to be considered under the condition of high-frequency laser echo scattered from multiple targets. Limited by insufficient hardware processing units and the requirement of increased measurement speed, a multi-target laser ranging based on matrix sparsification and a division-free Gauss-Jordan solver implemented on a field programmable gate array is proposed. A Jacobian matrix sparsification method is used to reduce the number of multiplication operations in the coefficient matrix and constant vector calculations, thereby reducing hardware resources and time costs. In order to increase the hardware implementation efficiency, a division-free Gauss-Jordan elimination method is used to quickly solve linear equations. The Vivado-based simulation results show that the amount of hardware resources, such as look-up tables, flip-flops and digital signal processor (DSP) are reduced by 34.5%, 35.7% and 27.3%, respectively, and the time cost is reduced by 3 µs (750 clock cycle @250 MHz) in the case of five iterations, satisfying the real-time requirements for a measurement rate of 45.45 kHz at most. Experimental results show that the proposed method maintains comparable performance of point extraction ability, ranging precision and accuracy, which are 100.0%, 1.78 cm and 0.62