NbMoTaW refractory high entropy alloy (RHEA) has excellent high temperature mechanical properties, but low room temperature ductility and high density severely limit its practical applications. In the present work, to overcome this deficiency, the composition was adjusted, and the mechanical properties of four novel as-cast NbMoTiZr-(Al/V) lightweight refractory high entropy alloys (LRHEAs) were investigated by theoretical calculations combined with experimental methods. The first-principle calculations approach based on density functional theory predicts the mechanical properties of LRHEAs and explains the alloying effects at the atomic and electronic levels. The body-centered-cubic (BCC) phase structure of the alloys were predicted on the formation enthalpy and cohesive energy, as well as empirical parameters such as ΔSmix, ΔHmix, VEC, and the atomic size difference, in conjunction with CALPHAD and XRD. The microstructure of the LRHEAs were also analyzed by SEM. The experimental results, along with the calculated elastic constants and moduli, show significant improvement in the strength and ductility of NbMoTiZr-(Al/V) LRHEAs compared to NbMoTaW RHEA. LRHEAs exhibit elastic anisotropy and are therefore more suitable for use in engineering applications. The strengthening mechanisms of the alloys were analyzed in terms of total and partial densities of states, overlapping Mulliken population, charge density contour and atomic distances. The increased plasticity of LRHEAs is mainly due to the formation of Ti-Ti, Zr-Zr and Zr-Al metallic bonds in the alloys. The calculated results agree with the experimental results, indicating that first-principles calculations are an effective method for predicting the improved properties of lightweight refractory high-entropy alloys. The present work provides a good guideline for the design and research of lightweight refractory high entropy alloys.