The speech envelope is essential for speech understanding and can be reconstructed from the electroencephalogram (EEG) recorded while listening to running speech. This so-called "neural envelope tracking" has been shown to relate to speech understanding in normal hearing listeners, but has barely been investigated in persons wearing cochlear implants (CI). We investigated the relation between speech understanding and neural envelope tracking in CI users. EEG was recorded in 8 CI users while they listened to a story. Speech understanding was varied by changing the intensity of the presented speech. The speech envelope was reconstructed from the EEG using a linear decoder. Next, the reconstructed envelope was correlated with the envelope of the speech stimulus as a measure of neural envelope tracking which was compared to actual speech understanding. This study showed that neural envelope tracking increased with increasing speech understanding in every participant. Furthermore behaviorally measured speech understanding was correlated with participant-specific neural envelope tracking results indicating the potential of neural envelope tracking as an objective measure of speech understanding in CI users. This could enable objective and automatic fitting of CIs and pave the way towards closed-loop CIs that adjust continuously and automatically to individual CI users.