Due to the limitations of traditional gratings, researchers began to look for new methods to fabricate gratings. In recent years, some interesting physical phenomena such as coherent population trapping, electromagnetically induced transparency, spontaneously generated coherence have attracted great attenton. If the standing wave field in the form of spatial modulation is replaced by the traveling wave field in the electromagnetically induced transparency effect, alternating high transmission regions and high absorption regions can be generated. The incident probe light diffracts after passing through the standing wave region, forming a grating-like structure which is named electromagnetically induced grating. Compared with traditional gratings, electromagnetically induced grating shows many advantages. For example, the amplitude and phase can be modulated simultaneously, and the grating constant, diffraction energy and diffraction order can be changed by adjusting the wavelength of the standing wave field, the intensity and detuning of the incident light fields. The concept of electromagnetically induced grating is first proposed theoretically in the three-level Λ-type atomic system. Subsequently, researchers experimentally observe and study the electromagnetically induced grating in cold atomic and hot atomic system successively. In order to improve the diffraction efficiency, more schemes have been proposed to realize electromagnetic induction grating in different atomic system, semiconductor quantum well and quantum dot system, and Rydberg atomic system, etc. In recent years, the research about electromagnetically induced grating has gradually developed to two-dimensional space. By using two orthogonal standing wave fields, two-dimensional electromagnetically induced cross grating can be realized in a tripod four-level atomic system. And some other researchers have then studied the electromagnetically induced grating in different two-level, three-level and four-level atomic system. In addition, P-T symmetry, Raman interaction, azimuth modulation of vortex field also are used to achieve high-efficiency two-dimensional electromagnetically induced grating. Due to its many advantages, electromagnetically induced grating has been applied in the research fields of photon and optical quantum devices such as all-optical switching and routing, coherent induced photonic band gap, quantum Talbot effect, beam splitting. In this paper, we propose a scheme to study two-dimensional electromagnetically induced grating in a four-level atomic system with double dark states. In our scheme, the microwave field is used to couple two dipole forbidden low-energy levels, and a weak probe field and a two-dimensional standing wave coupling field with periodic spatial intensity are used to drive the transitions between other energy levels, respectively. The Fraunhofer diffraction pattern and diffraction efficiency of the weak probe field are analyzed in the presence or absence of the microwave field. The results show that the existence of microwave field can weaken the zero order diffraction intensity, and significantly increase the first-order diffraction intensity and efficiency. To explain the physical mechanism more clearly, the plot of the refractive index part and the absorption part of the probe field polarizability with the probe detuning is given and disscused in the presence of microwave field. Then, the amplitude modulation and phase modulation are displayed, and the effect of corresponding modulation on Fraunhofer diffraction diagram is analyzed. The results show that the existence of microwave field has great influence on phase modulation. The incident light of the probe field diffracts toward higher order. High-order diffraction is mainly accomplished by phase modulation, but the diffraction energy of the grating controlled by amplitude modulation . At the same time, we discuss the influence of other system parameters, such as the detuning of the probe field, the intensity of the control field and the interaction length on diffraction pattern and diffraction efficiency of the grating in the presence of microwave field. The results show that, by properly tuning the system parameters, the two-dimensional electromagnetically induced grating with high diffraction efficiency can be realized in the system we studied. The scheme proposed can be applied to all-optical beam splitting and optical switching, which is potentially useful for research in optical information processing and optical network communication.