Objectives In recent years, there has been significant interest in recovering the temporal envelope of a speech signal from the neural response to investigate neural speech processing. The research focus is now broadening from neural speech processing in normal-hearing listeners towards hearing-impaired listeners. When testing hearing-impaired listeners, speech has to be amplified to resemble the effect of a hearing aid and compensate for peripheral hearing loss. Today it is not known with certainty how or if neural speech tracking is influenced by sound amplification. As these higher intensities could influence the outcome, we investigated the influence of stimulus intensity on neural speech tracking. Design We recorded the electroencephalogram (EEG) of 20 normal-hearing participants while they listened to a narrated story. The story was presented at intensities from 10 to 80 dB A. To investigate the brain responses, we analyzed neural tracking of the speech envelope by reconstructing the envelope from the EEG using a linear decoder and by correlating the reconstructed with the actual envelope. We investigated the delta (0.5–4 Hz) and the theta (4–8 Hz) band for each intensity. We also investigated the latencies and amplitudes of the responses in more detail using temporal response functions, which are the estimated linear response functions between the stimulus envelope and the EEG. Results Neural envelope tracking is dependent on stimulus intensity in both the TRF and envelope reconstruction analysis. However, provided that the decoder is applied to the same stimulus intensity as it was trained on, envelope reconstruction is robust to stimulus intensity. Besides, neural envelope tracking in the delta (but not theta) band seems to relate to speech intelligibility. Similar to the linear decoder analysis, TRF amplitudes and latencies are dependent on stimulus intensity: The amplitude of peak 1 (30-50 ms) increases, and the latency of peak 2 (140–160 ms) decreases with increasing stimulus intensity. Conclusion Although brain responses are influenced by stimulus intensity, neural envelope tracking is robust to stimulus intensity when using the same intensity to test and train the decoder. Therefore we can assume that intensity will not be a confounder when testing hearing-impaired participants with amplified speech using the linear decoder approach. In addition, neural envelope tracking in the delta band appears to be correlated with speech intelligibility, showing the potential of neural envelope tracking as an objective measure of speech intelligibility.