In this study, a computationally efficient ranging scheme exploiting a minimum mean square error (MMSE) and a matrix-pencil (MP) technique is proposed for the IEEE 802.15.4a chirp spread spectrum (CSS) system. Based on the characteristics of the CSS signal, a practical methodology for the MMSE process is devised and the appropriate values of parameters, which are cutoff bandwidth, number of samples and sampling duration in frequency domain, are investigated and numerically determined to enhance the performance. The performance of proposed scheme is analyzed in terms of the computational complexity and the ranging estimation errors. Simulation results demonstrate that the proposed scheme performs as well as the conventional scheme at remarkably reduced computational costs.