We propose a new power conversion system for a permanent magnet synchronous generator (PMSG) based grid-connected wind energy conversion system (WECS) operating with fully-controlled back-to-back current-source converters. On the generator side, two independent current-source rectifiers (CSRs) with space-vector pulse width modulation (SVPWM) are employed to regulate and stabilize DC-link currents. Between DC-link and the electrical grid, a direct-type three-phase five-level current-source inverter (CSI) is inserted as a buffer to regulate real and reactive power fed to the grid and thus adjusts the grid side power-factor. We also present a current-based maximum power point tracking (MPPT) scheme, which helps the generator extract the maximum power through closed-loop regulation of the generator speed. By applying the multilevel modulation and control strategies to the grid-side five-level CSI, a multilevel output current waveform with less distortion is produced, and the bulk requirement of the output capacitor filter to eliminate the harmonic current is reduced. All the proposed concepts are verified by simulation models built in a PSIM environment.