<p>The multiple-sets split feasibility problem (MSSFP) is to find a point in the intersection of finite closed and convex sets such that its image under a linear transformation belongs to the intersection of another finite closed and convex sets in image space. Recently, Taddele et al. [Optimization, 2022, 71(12): 3571-3601] proposed an efficient ball-relaxed projection algorithm to solve the MSSFP whenever each feasible set of MSSFP is a lower-level set of a strongly convex lower semi-continuous function. Inspired by Yao et al. [Optimization, 2020, 69(2): 269-281], we present a ball selected relaxation inertial projection algorithm (BSRIPA) for MSSFP. BSRIPA modifies the algorithm of Taddele et al. by using the selected two balls (one ball has the largest distance to the current iterate point and another ball has the largest distance to the image of the current iterate point) to generate the next iterate point. Comparing with the algorithm in Taddele et al., BSRIPA can save some projections onto the ball in each iteration. The inertial technique is also incorporated into BSRIPA. Moreover, BSRIPA takes a new step-size strategy, which is different from the step-size in Yao et al. The global convergence of the sequence generated by BSRIPA is established whenever the solution set is nonempty. Numerical experiments show that BSRIPA is more efficient than the algorithm in Taddele et al.</p>