Quantitative analysis of magnetic resonance signal lifetimes could reveal molecular scale information. However, it is non-trivial to recover the relaxation times from MR experiments in the multi-component exponential decay analysis. Constraints are required for the ill-posed problem in conventional inversion methods, which could lead to biased solutions. Artificial neural networks (ANNs) are a series of densely connected information processing nodes which cumulatively map a set of inputs to a set of outputs. They have proven to be universal approximators and powerful tools for solving complex nonlinear problems. In this work, ANNs were trained to recover T2 relaxation times. Both the discrete T2 spectrum and continuous T2 distribution were considered. Increased accuracy was achieved compared to the traditional methods. The continuous spectrum peak widths, generally not reliable in the traditional approach, could be determined accurately with ANN when the signal-to-noise ratio permitted.