We report the observation of a linear magnetoresistance in single crystals and epitaxial thin films of the pyrochlore iridate Bi2Ir2O7. The linear magnetoresistance is positive and isotropic at low temperatures, without any sign of saturation up to 35 T. As temperature increases, the linear field dependence gradually evolves to a quadratic field dependence. The temperature and field dependence of magnetoresistance of Bi2Ir2O7 bears strikingly resemblance to the scale invariant magnetoresistance observed in the strange metal phase in high Tc cuprates. However, the residual resistivity of Bi2Ir2O7 is more than two orders of magnitude higher than the curpates. Our results suggest that the correlation between linear magnetoresistance and quantum fluctuations may exist beyond high temperature superconductors.