<p>Complete characterization of a multimode optical process has paved the way for understanding complex optical phenomena, leading to the development of novel optical technologies. Until now, however, characterizations have mainly focused on linear optical processes, despite the importance of nonlinear optical processes for photonic technologies. Here we report the complete experimental characterization of multimode second-order nonlinear optical quantum processes—also known as bosonic Gaussian channels. Our resource-efficient characterization method, demonstrated on a 16-mode quantum process, captures the full information of non-unitary quantum evolution and satisfies the required physical condition. This complete characterization enables the identification of eigenquadratures and their associated amplification and noise properties. Moreover, we demonstrate the broad applicability of our method by characterizing various nonlinear optical quantum processes, including cluster-state generation, mode-dependent loss with nonlinear interaction and a quantum noise channel. Our method, by providing a versatile and efficient technique for characterizing a nonlinear optical process, will be beneficial for developing scalable photonic technologies.</p>