Trainable computer vision systems are receiving increased attention in different application domains for their versatility and flexibility. This paper describes a trainable system capable of determining fish weight from image measurements. A prototype of the proposed system has been experimentally installed as a component of an automatic fish grading device at a fish farm. The image measurements are taken from top and side views of live fish sliding through a transparent channel. After the training stage, in which a support vector machine learns the relation between fish weight and shape parameters from a small number of examples, the system is able to grade fish at the rate of three fish per second. The experimental results obtained thus far and reported in the paper indicate that the system is adequate for the required task.