Theoretical analysis of a stair‐shaped waveguide‐fed hemispherical dielectric resonator antenna (DRA) using method of moments (MoM) is presented in this study. Waveguide steps are used to enhance the coupling of direct coupled waveguide‐fed DRA. Theoretical analysis is performed by solving coupled integral equations obtained by imposing magnetic field boundary conditions at various apertures using MoM. DRA and the steps are analysed using Green's function. For waveguide, modal analysis is performed. In order to determine the effects of various design parameters, parametric analysis has been carried out using the code developed. Experimental results confirm the validity of the proposed theory. The antenna has a maximum gain of 5.7 dBi at 9.09 GHz with a 3 dB gain bandwidth of 11.08%. Reasonable agreement is observed between the measured and simulated radiation patterns. The proposed coupling enhancement technique guarantees more than 98% coupling.