The fluctuation theorems obtained in a stochastic Markovian process are generalized to anon-Markovian system governed by the non-linear generalized Langevin equation with aGaussian colored noise. We derive the non-Markovian version of the Crooks fluctuationtheorem that relates the statistical averages of the two different dynamics characterized bythe forward process and the reverse process. In contrast to the similar study by Zamponi et al, ours does not assume a stationary state asymptotically in time so that the presentfluctuation theorem can deal explicitly with the dependence of the initial condition and thetransient behavior. The Jarzynski equality for the non-equilibrium work relation and therepresentation of the linear response in the non-equilibrium steady state are also discussed.The conditions for the memory kernel that the fluctuation theorems hold are examined byanalyzing a solvable model and are confirmed by a direct derivation of the fluctuationtheorems for the cases of an exponential decay and a power law decay of the memorykernel.