Abstract <p>Numerical modeling of atmospheric dynamics presents significant challenges due to the multiscale nature of physical processes and the stringent computational requirements of operational weather forecasting and climate modeling. Implicit treatment of terms representing fast wave dynamics is widely employed to address stiffness in atmospheric models. However, this approach requires solving large systems of linear algebraic equations (SLAEs) at each time step, necessitating efficient and scalable solvers. Multigrid methods are among the most effective approaches for solving elliptic problems, but their efficiency is highly dependent on the underlying spatial discretization. In particular, the use of collocated schemes results in odd-even decoupling (checkerboard instability) when applied to fluid dynamics equations, undermining the performance of standard geometric multigrid methods. In this work, we propose a novel geometric multigrid solver designed for SLAEs arising from collocated discretizations of atmospheric dynamics equations. By leveraging the inherent odd-even decoupling, we introduce specialized intergrid transfer operators that maintain the efficiency of standard multigrid methods. This approach achieves robust convergence without requiring modifications to other multigrid components, as validated through 1D analysis and numerical experiments on the cubed-sphere grid. Our results demonstrate high convergence speeds for both 2/1 and 4/2-order Summation-by-Parts Finite Difference (SBP FD) approximations, with the solver being robust across different parameter configurations. Additionally, we show that the proposed solver achieves nearly identical convergence rates as staggered grid solvers, while maintaining parallel efficiency. This work provides a practical and efficient solution for collocated schemes in atmospheric modeling, paving the way for their broader adoption in next-generation weather and climate models.</p>