The plasmon resonance and electric field enhancement in a side-by-side tangent nanospheroid homodimer (TNSHD) have been investigated theoretically by using DDA and FDTD methods, respectively. The simulation results indicate that this side-by-side TNSHD has its novel optical properties. We find that the plasmon resonance with a distinct Fano lineshape can be achieved and the electric field intensity can be enhanced strongly. The tunability of the Fano resonance could provide important applications in biosensing. The obtained electric field enhancement might open a promising pathway for surface-enhanced Raman scattering (SERS) and light trapping in solar cells.