Photovoltaic (PV) monitoring and fault detection are very crucial to enhance the service life and reliability of PV systems. It is difficult to detect and classify the faults at the Direct Current (DC) side of PV arrays by common protection devices, especially Line-to-Line (LL) faults, because such faults are not detectable under high impedance fault and low mismatch conditions. If these faults are not diagnosed, they may significantly reduce the output power of PV systems and even cause fire catastrophe. Recently, many efforts have been devoted to detecting and classifying LL faults. However, these methods could not efficiently detect and classify the LL faults under high impedance and low mismatch. This paper proposes a novel fault diagnostic scheme in accordance with the two main stages. First, the key features are extracted via analyzing Current-Voltage (I-V) characteristics under various LL fault events and normal operation. Second, a genetic algorithm (GA) is used for parameter optimization of the kernel functions used in the Support Vector Machine (SVM) classifier and feature selection in order to obtain higher performance in diagnosing the faults in PV systems. In contrast to previous studies, this method requires only a small dataset for the learning process and it has a higher accuracy in detecting and classifying the LL fault events under high impedance and low mismatch levels. The simulation results verify the validity and effectiveness of the proposed method in detecting and classifying of LL faults in PV arrays even under complex conditions. The proposed method detects and classifies the LL faults under any condition with an average accuracy of 96% and 97.5%, respectively.