Automatic modulation classification (AMC) facilitates adaptive modulation schemes, leading to the minimization of pilot signals, thus affecting spectral efficiency and reducing the power consumption in wireless communications systems. Since high-frequency heterogeneous and adaptive networks are established as future projections, AMC will also play a critical role in the millimeter-wave (mmWave) band communications. This study proposes multi-channel convolutional long short-term deep neural network (MCLDNN) model for AMC in mmWave bands. The performance of the proposed method is evaluated under real conditions based on a measurement campaign. 802.11ad signals are utilized for the measurements in 57.24 GHz to 59.40 GHz band. The classification performance of the proposed model is compared with that of well-known deep-learning methods, i.e., convolutional neural network and convolutional long short-term deep neural network. The measurement results imply the robustness of the proposed method to real-life conditions and its superiority against contemporary networks, especially in low signal-to-noise ratio (SNR) region.