In this paper, a dual band dual circularly polarized microstrip antenna for 28/60 GHz applications is presented. This antenna is designed to be used in hand-held devices for both 5G and WiGig applications simultaneously. The circular polarization in this case represents an important advantage to avoid polarization mismatch at different orientations. The proposed antenna consists of two parts: an annular ring around a circular patch with slot perturbations in both of them. The two parts of the proposed antenna are resonant at different frequencies. The inner circular patch is designed to be resonant around the 60 GHz band while the annular ring is designed to be resonant around the 28 GHz band. These two parts are simultaneously excited by an arc-shaped strip. Each part of this antenna structure operates as a single band circularly polarized radiator. The circular polarization is obtained by exciting orthogonal modes in each part of this antenna configuration with equal amplitudes and 90° phase shift. These orthogonal modes are obtained by introducing perturbations in both the inner circular disk and the outer annular ring. These perturbations are shifted by 45° from the location of the feeding arc. However, these perturbations affect the matching properties of designed antenna. Thus, a meander line stub is connected to the annular ring to adjust the matching of the designed antenna. The characteristics of the proposed antenna are designed and simulated by using full-wave EM simulator CST Microwave Studio and High Frequency Structural Simulator (HFSS).