An analytical method to predict the elastic modulus of the sandwich body-centered cubic (BCC) lattice structure is presented on the basis of the assumption of a linearly changing elastic modulus. In the constrained region, the maximum of elastic modulus used the elastic moduli of the BCC lattice element with plate constraints and is calculated with Timoshenko beam theory, the minimum used without plate constraints. In the rest of the constrained region, a linear function along the thickness direction is proposed to calculate elastic modulus. The elastic modulus of the unconstrained region is constant and it is the same as the minimum of the constrained region. The elastic modulus of the whole sandwich BCC lattice structure can be calculated theoretically with the elastic modulus of the constrained and unconstrained regions and a single-layer slice integration method. Six kinds of sandwich BCC lattice structures with different geometric parameters are designed and made by resin 3D printing technology, and the elastic moduli are measured. By comparing the predictions of the elastic modulus using the proposed analytical method and existing method with experimental results, the errors between the results of the existing method and the experimental results varied from 10.3% to 24.7%, and the errors between the results of the proposed method and the experimental results varied from 1.6% to 7.4%, proving that the proposed method is more accurate than the existing methods.