The minimum variance (MV) beamformer, also known as the Capon or minimum variance distortionless response (MVDR) beamformer, uses the recorded wavefield to compute a set of optimal weights to be applied to each sensor, before coherently adding the sensor outputs. The weights are chosen such that the variance of the output is minimized while maintaining unit gain in the view direction. The MV beamformer offers improved resolution and image quality compared to the conventional delay-and-sum (DAS) beamformer. The MV beamformer was originally introduced for passive systems. When adapting the MV beamformer to active sonar, sub-array averaging is necessary in order to avoid signal cancellation of coherent signals, and to reduce the sensitivity to errors in the wavefield parameters. Sub-array averaging is a technique developed for flat, uniformly sampled arrays, and it is not immediately evident that this will give satisfactory results on a non-flat array. In this work, we have successfully implemented the MV beamformer on an active 1D circular sonar array suitable for fishery sonar. We demonstrate, through simulations, that it is feasible to apply the MV beamformer with sub-array averaging to a circular array. Our results have been verified using experimental data from the Simrad SX90 fishery sonar.