Flux Balance Analysis (FBA) is a widely used approach for studying biochemical networks, and in particular the genome-scale metabolic network reconstructions. It formulates the problem of predicting a cell's chemical reaction fluxes as the linear optimization problem of maximizing a cellular objective (e.g., growth) subject to constraints capturing stoichiometry mass balances of the metabolic network and bounds that reflect the composition of the growth medium. In practice, however, reaction fluxes of the cells under specific growth conditions are available to be measured, but the primal FBA objective function is not necessarily known. Understanding its structure can elucidate the cellular metabolic control mechanisms and infer important information regarding an organism's evolution. To that end, we have developed an Inverse Flux Balance Analysis (InvFBA) method which is a novel inverse optimization-based framework for inferring metabolic objective functions. Within this framework, we present three different forms of objective functions: linear, quadratic, and non-parametric. We show that in all cases, the inverse problem is tractable and can be solved efficiently. We provide several numerical examples to show that the inference of the objective function is consistent with simulated flux data and actual measurements.