Using the first-principles calculations, a cluster-plus-glue-atom model was employed to investigate the elastic and electronic properties of Ti-Mo-Nb alloys with cluster formula of [MoTi14] (glue atom) (x) (glue atom = Ti, Mo, Nb, x = 1 or 3) for a theoretical guidance in composition design of beta titanium alloys. The bulk modulus, shear modulus, Young's modulus, and Poisson ratio were evaluated from the calculated elastic constants using Voigt-Reuss-Hill average scheme on the periodic supercell model of cluster packing. The electronic properties of the Ti-Mo-Nb alloys were discussed by analyzing the electron density of state and Mulliken population. Meanwhile, we designed two series of Ti-Mo-Nb alloys, i.e., [MoTi14]X-1 (X = Ti, Mo, Nb) and [YTi14]Nb-3 (Y = Ti, Mo), and experimentally measured their mechanical properties. Our theoretical results (including mass density, Young's modulus, ductility) based on our cluster packing model agreed well with the experimental data, especially for [TiMo14]X-1 (X = Ti, Mo, Nb) alloy series. On the contrary, the random solid solution structures were mechanically unstable and the calculated values significantly deviated from the experiments. Based on the cluster-plus-glue-atom model, an Ashby map of E/rho versus B/G was constructed and indicated the inverse correlation between stiffness and ductility, for which the random solid solution model was unable to reflect. The Mo/Ti = 1/14 rule derived from the cluster model may serve as an important guideline for composition design of Ti-Mo based systems to achieve low elastic modulus alloys with stable beta phase.