A new approach based on deep learning techniques for multidimensional codebook (MDC) design over Rayleigh fading channels is proposed in this letter. Different from autoencoder (AE) techniques, the proposed deep neural network (DNN) can generate codebooks directly without a decoder structure. Two loss functions, one exploiting essential figures of merit (FoMs) and the other based on theoretical symbol error probability over fading channels, are introduced for the proposed DNN structure. Simulation results reveal that the resulting codebooks of the proposed approach have similar symbol error rate (SER) performance when adopting different loss functions. They have substantial SER performance gain over the codebooks learned by AEs, and reach close SER performance with codebooks conventionally designed by state-of-the-art. Moreover, the proposed approach guarantees good FoMs for the learned MDCs.