In this correspondence paper, we consider a cell-free massive Multiple-Input Multiple-Output (MIMO) system where access points (APs) serve a much smaller number of users under the time-division duplex operation. The APs first estimate the channels via the uplink training phase. Then, these channel estimates are used to detect desired symbols in the uplink and precode the transmit symbols in the downlink. Nonorthogonality of pilot sequences and AP selection (e.g., received-power-based selection or largest-large-scale-fading based selection schemes) are taken into account. To reduce the effect of pilot contamination, we propose a pilot power control design, which chooses the pilot power control coefficients to minimize the mean-squared error of the channel estimation. This is achieved via the sequential convex approximation method. By using pilot power control in training phase, the system performance is considerably improved. In addition, we derive closed-form expressions for the uplink and downlink achievable rates with arbitrary power data/pilot control coefficients and any AP selection schemes.