In this paper, a new interleaved DC-DC converter based on a coupled and a single input inductor is proposed. The suggested high step-up converter utilizes various inductive and capacitive methods to transfer magnetic energy more efficiently. The output voltage is regulated with the switches' duty cycle and the coupled inductor (CI) turns ratio, which provide a wide output voltage range. Interleaving improves the converter reliability, employs both the first and third areas of CI's B-H plane, cancels DC component of the CI, and reduces the input current ripple of the proposed converter with twice switching frequency. Utilization of two output ports for voltage stress and ripple reduction in each port, recycling the stored energy of inductances in both forward and flyback mechanisms, alleviation of switch voltage spikes, operation without circulating current, high power density, independency of switch voltage stress to the CI turns ratio, and continuous input current can be mentioned as other features. In this paper, continuous and discontinuous conduction modes' steady-state analytics, power loss calculations, and design procedure of the proposed converter are followed with comprehensive comparisons to evaluate the capabilities. Eventually, experimental results are presented to validate theoretical calculations.