This paper presents an effective planning methodology for electric vehicle (EV) fast-charging stations (CS) using a multi-objective binary version of the atom search optimization (ASO) algorithm. The proposed method uses quantum operations to binarize the algorithm and achieve a higher convergence rate than the existing binary ASO algorithm. Additionally, a modified atom selection function is used to improve the searching capability of the ASO algorithm. Furthermore, the nondominated sorting procedure and pareto concepts are infused to solve the CS location problem (CSLP) considering the EV travel time, CS costs, and grid power loss as independent multi-objectives. The efficacy of the proposed multi-objective quantum ASO (MO-QASO) algorithm is evaluated using performance metrics namely, inverted generational distance (IGD), spacing (SP), and maximum spread (MS). The MO-QASO simulation results are compared with the results of other heuristic algorithms. MO-QASO achieves the best IGD (0.0021), SP (0.0002), and MS (0.9982) values, verifying the convergence and diversity of the algorithm. Importantly, the best CS planning solution obtained from MO-QASO is similar to the true solution obtained from the exhaustive search method. The MO-QASO efficiency is further validated by solving a CSLP from literature. Thus, the MO-QASO algorithm is a promising optimization tool for solving CSLP.