Crystal structure and magnetic properties of the Co2Mn1-x V-x Sb (0 <= x <= 1) Heusler compounds have been studied by X-ray powder diffraction (XRD), magnetometric measurements, and full-potential linearized augmented plane wave (FP-LAPW) method. All compounds crystallize in a cubic Cu2MnAl-type crystal structure with the space group Fm-3m. The samples for x < 0.8 have the Curie temperatures above room temperature, while the Curie temperature is observed at 68 K for the sample with x = 0.8. The saturation magnetization at 5 K decreases linearly with increasing vanadium concentration x. The values of the saturation magnetization obtained by FP-LAPW-local density approximation (LDA) calculations are in better agreement with the experimental results compared with the results obtained by FP-LAPW-generalized gradient approximation (GGA) calculations.