<p>The improved discrete velocity method (IDVM), a multiscale kinetic approach, solves both the Boltzmann model equation and the macroscopic governing equations. It maintains the simplicity of the conventional discrete velocity method while significantly enhancing accuracy and efficiency in the continuum flow regime. However, previous implementations of IDVM were limited to monatomic gases, rendering it inapplicable under real atmospheric conditions dominated by diatomic gases. In this paper, the fully implicit IDVM is extended to the Boltzmann-Rykov model equation to simulate multiscale gas flows involving the rotational non-equilibrium effects of diatomic molecules. This approach incorporates macroscopic governing equations to predict the equilibrium distribution function, enabling the fully implicit discretization of the Boltzmann-Rykov model equation and ensuring rapid convergence. Numerical simulations are performed for several cases, including the one-dimensional nitrogen shock tube, two-dimensional flows around a flat plate and a blunt circular cylinder, and three-dimensional supersonic flow over a sphere. The results of the present algorithm show remarkable alignment with those from similar kinetic algorithms and experimental data, demonstrating its ability to simulate non-equilibrium diatomic gas flows. Relative to the conventional semi-implicit discrete velocity method and implicit kinetic methods with a macroscopic forecasting technique, the proposed approach attains varying degrees of acceleration.</p>