Even though there exist significant advances in recent studies, existing methods for pedestrian detection still have shown limited performances under challenging illumination conditions especially at nighttime. To address this, cross-spectral pedestrian detection methods have been presented using color and thermal, and shown substantial performance gains on the challenging circumstances. However, their paired cross-spectral settings have limited applicability in real-world scenarios. To overcome this, we propose a novel learning framework for cross-spectral pedestrian detection in an unpaired setting. Based on an assumption that features from color and thermal images share their characteristics in a common feature space to benefit their complement information, we design the separate feature embedding networks for color and thermal images followed by sharing detection networks. To further improve the cross-spectral feature representation, we apply an adversarial learning scheme to intermediate features of the color and thermal images. Experiments demonstrate the outstanding performance of the proposed method on the KAIST multi-spectral benchmark in comparison to the state-of-the-art methods.