A theoretical model for a deforming single droplet with aerodynamic force is presented. The droplet shape is assumed to be spheroidal. A nonlinear oscillating equation is derived from energy conservation in a droplet. The present (OSD) model is compared with other droplet deformation models, Taylor Analogy Breakup (TAB), Droplet Deformation Breakup (DDB) and Synthesized Spheroidal Particle (SSP) models. It is found that the linearized OSD model is reduced to the TAB model. Numerical studies show that only present model and TAB model are compatible with Lamb's fundamental oscillating mode for a liquid droplet. On a droplet deformation at the initial stage of aerodynamic breakup, the calculation by the OSD model and TAB model agree well with the measurement.