We systematically study the stability, Gilbert damping parameters, electronic structure, exchange interaction and Curie temperature of CrYCoZ (Z = Al, Ga, In, Tl) alloys. Stability is estimated from the perspective of thermodynamics, dynamics and mechanics. Gilbert damping parameters are calculated by using the linear response formalism, and the values 0.6~& nbsp;4.1 x 10(-3) are observed at room temperature. Electronic calculations show that the CrYCoZ alloys are half-metallic ferrimagnets, and their integer magnetic moments follow the M-t = Z(t) - 18. Origin of gap is discussed by the hybridization, distribution and occupation of electronic states as well as the charge transfer. In addition, the effect of GGA+U on electronic structure is also discussed. Based on the Heisenberg model, we calculate the exchange interactions between atomic components, and analyze the competition and collaboration between d-d exchange, super-exchange and RKKY exchange, finally offer the dominant mechanism of appearance of ferrimagnetic order phase. Furthermore, we calculate the Curie temperatures of CrYCoZ alloys, which are much higher than room temperature. Overall, the CrYCoZ alloys can be considered as a prospective candidates in spintronics application.