We have evaluated the shear viscosity of pion gas with vanishing chemical potential taking into account its scattering with the low mass resonances sigma and rho during propagation in the medium. The thermal width (or collisional rate) of pions is calculated from pi sigma and pi rho loop diagrams using effective interactions in the real-time formulation of finite temperature field theory. A very small value of shear viscosity by entropy density ratio (eta/s), close to the quantum bound, is obtained which approximately matches the range of values eta/s used by Niemi et al. [H. Niemi, G. S. Denicol, P. Huovinen, E. Molnar, and D. H. Rischke, Phys. Rev. Lett. 106, 212302 (2011); Phys. Rev. C 86, 014909 (2012)] to fit the elliptic flow data from the Relativistic Heavy Ion Collider.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Univ Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, BrazilCtr Variable Energy Cyclotron, Div Theoret Phys, Kolkata 700064, IndiaUniv Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, BrazilFAPESP: 09/50180-0FAPESP: 12/16766-0FAPESP: 13/01907-0CNPq: 305894/2009-9