In this paper, an effective pilot assignment algorithm is proposed to counter the pilot contamination (PC) issue caused by limited pilot sequences during massive access in a user-centric cell-free massive multiple-input multiple-output system. The problem of pilot assignment is formulated as max-min spectral efficiency (SE) optimization problem which is NP-hard. Hence, the paper proposes a heuristic-based algorithm to assign pilots to users (UEs) in such a way that the repetitive assignment among the associated UEs for all the access points can be avoided. Numerical results demonstrate that the proposed algorithm achieves up to 37% average SE gain while reducing the interference power by up to 52% relative to the random and two state-of-the-art pilot assignment schemes. Moreover, the proposed pilot assignment scheme exhibits the best balance in the trade-off between the performance criteria and the computational complexity relative to its comparatives.