Recently we have applied a classical split perfectly matched layer (PML) to the second-order scalar arbitrarily wide-angle wave equation (AWWE) in terms of displacement. However, the classical split PML increases computational cost obviously and has a poor performance at grazing incidence. The unsplit convolutional PML (CPML) has been proven to be more efficient in absorbing evanescent waves and propagating waves at grazing incidence. We reformulate the original AWWE as a first-order formulation and incorporate the CPML into the renewed formulation. The staggered-grid finite-difference (SGFD) method is adopted to discretize the first-order system. The presented first-order AWWE with the CPML is confirmed to be computationally more efficient than the original second-order AWWE with the classical split PML in wavefield depth continuation. Several numerical examples are presented to prove correctness of the SGFD method and the absorption effect of the CPML in AWWE numerical simulation and migration.