We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with reverse dynamic method (known in literature as “adjoint method”) to train neural ODEs on classification, density estimation and inference approximation tasks. We also propose a theoretical justification of our approach using logarithmic norm formalism. As a result, our method allows faster model training than the reverse dynamic method what was confirmed and validated by extensive numerical experiments for several standard benchmarks.