In this work, using the theory of functional density (DFT), we studied theelectronic structure, elastic and the magnetic of quaternary full-Heusler alloys Cr2NbGe1-xSnx . The calculations of the structural parameters, electronic structure and partialdensity of state (PDOS) are performed using the full-potential linearized augmented plane wavemethod with the Generalized Gradient Approximation (GGA) as functional of exchangeand correlation. Our investigations show that Cu2MnAl-type structures of the Cr2NbGe1-xSnx (x = 0, 0.25, 0.50, 0.75, 1.00) Heusler compounds are more stable than that of Hg2CuTi-type ones.The elastic constants results show that these compounds are mechanically stable. These Heusler alloys are found to be a complete half-metal with a total magneticmoment of -3.00 μB, the origin of magnetic moment is due to the exchange splitting of Nb-dand Cr-d states. The quasi-harmonic Debye model, as implemented in the Gibbs code, was used to predict the thermal properties of the Cr2NbGe1-xSnx . These alloys seem to be apotential candidate of spintronic devices