This paper introduces the chirped cosh-Gaussian vortex beam(CCGVB) and investigates its propagation in uniaxial crystal. The received field is obtained benefiting from the Huygens-Fresnel integral. In addition, analysis of the received field is carried out considering the variations in displacement parameter, chirped parameter, decay factor, and topological charge. Our results show that chirped parameter and decay factors place the beam in an off-axis position. These results can be beneficial for the design of optical communication systems, laser weapons, laser designators, and optical tracking while applying beam shaping.