In this paper, using the recent method proposed by Ono, Ishihara and Asada (OIA) who extend the idea of Gibbons and Werner to the stationary and axisymmetric case, we apply the Gauss-Bonnet theorem to the optical metric of the non-rotating and rotating Damour-Solodukhin wormholes spacetimes to study the weak gravitational lensing by these objects. Furthermore, we study the strong gravitational lensing by the nonrotating Damour-Solodukhin wormholes using the Bozza's method to see the differences between the weak lensing and the strong lensing. We demonstrate the relation between the strong deflection angle and quasinormal modes of the Damour-Solodukhin wormholes. Interestingly it is found that the wormhole parameter λ, affects the deflection of light in strong and weak limits compared to the previous studies of gravitational lensing by Schwarzschild black holes. Hence, the results provide a unique tool to shed light on the possible existence of wormholes.