The millimeter-wave (mm-wave) radio-over-fiber (RoF) systems have been widely studied as promising solutions to deliver high-speed wireless signals to end users, and neural networks have been studied to solve various linear and nonlinear impairments. However, high computation cost and large amounts of training data are required to effectively improve the system performance. In this paper, we propose and demonstrate highly computation efficient convolutional neural network (CNN) and binary convolutional neural network (BCNN) based decision schemes to solve these limitations. The proposed CNN and BCNN based decision schemes are demonstrated in a 5 Gbps 60 GHz RoF system for up to 20 km fiber distance. Compared with previously demonstrated neural networks, results show that the bit error rate (BER) performance and the computation intensive training process are improved. The number of training iterations needed is reduced by about 50 % and the amount of required training data is reduced by over 30 %. In addition, only one training is required for the entire measured received optical power range over 3.5 dB in the proposed CNN and BCNN schemes, to further reduce the computation cost of implementing neural networks decision schemes in mm-wave RoF systems.