Error minimization using conventional backpropagation algorithm for training feed forward neural network (FNN) suffers from problems like slow convergence and local minima trap. Here in this paper gradient free optimization is used for error minimization to avoid local minima. Hence we introduce a new hybrid algorithm integrating the concepts of physics inspired gravitational search algorithm and biology inspired flower pollination algorithm. Gravitational search algorithm is a novel meta-heuristic optimization method based on the Newtonian law of gravity and mass interaction, whereas flower pollination algorithm is an intriguing process based on the pollination characteristics of flowering plants. Gravitational search algorithm efficiently evaluates global optimum but it suffers from slow searching speed in the last iterations. Flower pollination algorithm exhibits faster searching but suffers from local minima due to the switch probability. Experimental results show that hybrid FP-GSA outperforms both FPA and GSA for training FNNs in terms of classification accuracy.