This paper proposes a path mismatch detection and compensation algorithm with the closed form solution for LInear Amplification with Non-linear Components (LINC) system implementation. The LINC system has a merit of using the high efficient amplifier. However, the performance degradation is extremely sensitive to the path mismatch such as amplitude as well as phase mismatch of transfer functions of two signal paths. In this work, a method with the closed form solution is developed that predicts the exact mismatch value without iterations. The LINC system is realized with the proposed mismatch detection and compensation algorithm. The performance was evaluated using the Orthogonal Frequency Division Modulation (OFDM) signal, which has 7 MHz channel bandwidth. The 20 dB Adjacent Channel Power Ratio (ACPR) improvement was obtained with the proposed detection algorithm.