We consider images of boar spermatozoa obtained with an optical phase-contrast microscope. Our goal is to automatically classify single sperm cells as acrosome-intact (class 1) or acrosome-damaged (class 2). Such classification is important for the estimation of the fertilization potential of a sperm sample for artificial insemination. We segment the sperm heads and compute a feature vector for each head. As a feature vector we use the gradient magnitude along the contour of the sperm head. We apply learning vector quantization (LVQ) to the feature vectors obtained for 320 heads that were labelled as intact or damaged using stains. A LVQ system with four prototypes (two for each class) allows us to classify cells with an overall test error of 6.8%. This is considered to be sufficient for semen quality control in an artificial insemination center.