Computational low frequency extrapolation is in principle the most direct way to address the cycle skipping problem in full waveform inversion (FWI). We propose a method of extrapolated full waveform inversion (EFWI), where FWI is allowed to make use of data augmented by increasing its frequency band with a convolutional neural network (CNN). In extrapolated FWI with CNN (EFWI-CNN), the low-wavenumber components of the model are determined from the extrapolated low frequencies, before proceeding with a frequency sweep of the bandlimited data. The proposed deep-learning method of low-frequency extrapolation shows adequate generalizability for the initialization step of EFWI. Numerical examples show that the neural network trained on several submodels of the Marmousi model is able to predict the low frequencies for the BP 2004 benchmark model. Additionally, the neural network can robustly process seismic data with uncertainties due to the existence of noise, unknown source wavelet, and different finite-difference scheme in the forward modeling operator.