We present results from non-interferometric quantitative phase imaging (QPI) for thickness estimation and morphological analysis of human spermatozoa. QPI along with algorithms for image processing enable localization and quantification of subcellular structures of spermatozoa, including the acrosomal, nuclear, mid-piece, and tail regions. This approach based on the transport of intensity equation (TIE) using a simple brightfield microscope renders quantitative phase image with nanometric depth sensitivity, allowing the precise subcellular structural resolution of human spermatozoa. We demonstrate the potential of TIE in real-time phase imaging and the morphological analysis of spermatozoa. We first calibrate the TIE using microbeads and a standard phase target of known dimensions. Image processing for quantitative volume estimation of nuclei and acrosomal regions is carried out on the reconstructed quantitative phase images. We also apply a Hilbert transform-based image processing algorithm to the retrieved phase for visualization of vacuoles present on the sperm head. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.