In this paper, in order to effectively eliminate the pilot contamination in cell-free massive multiple-input multiple-output (MIMO) systems, the pilot contamination precoding (PCP) method is applied by means of introducing the power scaling factor. The key idea of the PCP method is that central processing unit (CPU) linearly combine symbols for a fraction of user equipments (UEs) that reusing the same pilot sequence. Specifically, the achievable downlink UE spectral efficiency (SE) with PCP and conjugate beamforming (CB) preprocessing are derived based on the defined combination factors and power scaling factors. The derived expression is versatile for downlink UE SE whether PCP is used or not, which also facilitates analyzing the impacts of key system parameters. Finally, simulation results are provided to demonstrate the superiority of adopting the PCP method.