We report on a study of Nernst effect in an iron-based superconductor Fe_1+yTe_1-xSe_x. We observe a zero-field Nernst effect that appears around the superconducting transition temperature T_c. This spontaneous Nernst signal does not follow the temperature and field dependence of the thermal power and occur only in the temperature range near T_c where the superconducting fluctuation is strong and vortex liquid is robust. This intrinsic spontaneous Nernst signal indicates the violation of time reversal symmetry (TRS) in the superconducting state. The TRS in Fe_1+yTe_1-xSe_x may be broken by pinning flux introduced by the interstitial iron impurity. To further understand the role of excess Fe atoms, we study a series of Fe_1+yTe_1-xSe_x single crystals that have different T_c and different levels of excess Fe concentrations and demonstrate how they affect the spontaneous Nernst effect signal.