We propose a coherent lightwave neural network system whose behavior can be controlled by the lightwave carrier frequency. We utilize the dependence of homodyne interference on the lightwave frequency by choosing the optical path lengths of the signal and the reference to be slightly different. The synaptic weights consist both of the optical path difference and variable delay realized by a spatial light modulator. A frequency-dependent learning is performed by a novel complex-valued Hebbian rule associated with the carrier frequency. Experiments demonstrate that the associative memory recalls different complex-amplitude patterns according to the carrier frequency variation successfully.