We study the two-body charmed nonleptonic weak decays of the bottom meson to an axial-vector meson and a pseudoscalar meson using the non-relativistic quark model. We employ the factorization hypothesis to obtain the branching ratios of these decays. First, we calculate the axial-vector ($J^P=1^{+}$) emitting form factors for $B\to D_1/{\underset{\_}{D}}_1$ transitions in the non-relativistic Isgur-Scora-Grinstein-Wise quark model. Later, we use the heavy quark symmetry constraints to obtain the $B\to D_1^{1/2}/D_1^{3/2}$ form factors and consequently, calculated their branching ratios. For a comparative analysis, we extract ${\tau }_{1/2}\left(\omega \right)$ and ${\tau }_{3/2}\left(\omega \right)$ form factors from the recent lattice QCD results to get a qualitative estimate of $B\to D_1^{1/2}/D_1^{3/2}$ form factors. We find that the calculated branching ratios are in fair agreement with the available experimental data in both the scenarios. Also, we observe that, despite of $1/m_Q$ suppression in heavy quark limit, the color-suppressed contribution to these decays can not be ignored.