The hybrid modular multilevel converter with cascaded full bridges (HMMC-CFB) is a recently proposed dc fault tolerant converter topology for high-power applications. It has a director part (DP) consisting of a series of connected half-bridge submodules, and a wave-shaping part (WSP) composed of a series of connected full-bridge submodules (FBSMs). The submodules in DP avoid high voltage stresses and improve synchronization between DP and WSP by slowing down the change rate of DP output voltage. This slowdown is achieved by using a trapezoidal reference signal for DP. The WSP attenuates the voltage harmonics produced by DP. However, the energy exchanged by WSP changes with modulation index, which may cause improper voltage regulation of the submodule capacitors. This paper proposes a new control technique to regulate the energy exchanged by WSP, which uses a variable slope trapezoidal reference signal of DP. To obtain this slope, the feedforward and feedback controllers are used. The feedforward controller gives the value of slope depending on the modulation index ( mv ) to keep the energy exchanged by WSP nearly equal to zero, whereas the losses and nonideality of the converter are taken care of by the feedback controller. This technique guarantees proper voltage regulation of the submodule capacitors for all modulation indices. The efficacy of the proposed technique is confirmed using simulations and experimentations. This paper also presents a circulating current suppressing controller for HMMC-CFB. The proposed control schemes and dc fault tolerant capability of HMMC-CFB are tested on a grid-connected model built in PSCAD.