A novel framework for super-resolution direction of arrival (DOA) estimation of acoustic sources in the spherical harmonics (SH) domain has been addressed in this work. The proposed method is developed in two stages. First, a convolutional neural network (CNN) model is investigated to obtain the DOA classes from the spherical harmonics decomposition (SHD) of the spherical microphone array (SMA) recordings. Subsequently, the matching pursuit (MP) algorithm with a high-resolution search grid corresponding to the DOA classes is applied to the SHD signals to localize the acoustics source. Since the CNN model performs better in the noisy and reverberant environment and the MP algorithm uses the orthogonal property of the SH basis function to provide high-resolution localization, the proposed hybrid model takes advantage of both these models. Extensive simulations and real-time experiments are performed to validate the performance of the proposed model.