This work addresses the problem of implementing a model predictive control (MPC) scheme that embeds a parallel hybrid subspace model as the predictive component of the control strategy. The hybrid model considered here is inspired by the framework proposed by Ghosh et al. (Hybrid Modeling Approach Integrating First-Principles Models with Subspace Identification. Ind. Eng. Chem. Res. 2019, 58, 13533-13543), but it is adapted to make it amenable to online control. In particular, the framework uses a first-principles model and a subspace-based residual model (built with error between the process measurement data and the first-principles output of historical batches) in a parallel fashion. The present manuscript adapts this framework in a way that retains the linearity of the model utilized within the MPC. This is achieved by first building a subspace model (built with output data of the first-principles model) and then appending it with the residual model to have the same parallel hybrid model structure. This linear hybrid MPC is applied on a seeded batch crystallization process to reduce the volume of fines or crystals generated due to nucleation during the crystallization process, while maintaining a desired product quality at batch termination. The closed-loop results using the proposed control methodology are compared with a purely data-driven subspace-based model predictive controller.