In this cosmological model, we have studied the spatially homogeneous and anisotropic Bianchi type and axially symmetric model filled with dark matter and dark energy in Brans-Dicke’s [1] theory of gravitation. Here, we consider the modified holographic Ricci dark energy defined by Chen and Jing [21] as the suitable condition of dark energy. To obtain a solution we assumed the scale factor used Mishra et al. [43]. We have solved field equations of Brans-Dicke theory of gravitation with the help of an axially symmetric anisotropic Bianchi-type space-time. We have determined the cosmological parameters, namely, EoS parameter, MHRDE density, matter density, skewness parameter, and BD scalar field. Here the various phenomena like the expanding universe, and shift from anisotropy to isotropy are observed in this model. A detailed physical discussion of these dynamical parameters are presented graphically. Some physical and geometrical behaviours of the models are also discussed and found to be in good agreement with the recent observations (OHD+JLA) datasets.