Microphone arrays are becoming increasingly popular for conferencing applications and near-field speech recording. In this work, a 16-element cylindrical microphone array is designed for beamforming towards a nearby speaker, while reducing the influence of competing talkers. A two-stage approach is used to obtain the desired array directivity pattern, optimizing both microphone locations and filter weights. The positions of the microphones are optimized by using a hybrid optimization technique, taking into account the influence of the nearby acoustic environment. FIR filter coefficients for each microphone are derived from a regularized least-squares (LSQR) solution, combined with null-steering. The performance of the design is evaluated experimentally and compared with a classically used goose-neck microphone.