Facial morphs created between two identities resemble both of the faces used to create the morph. Consequently, humans and machines are prone to mistake morphs made from two identities for either of the faces used to create the morph. This vulnerability has been exploited in “morph attacks” in security scenarios. Here, we asked whether the “other-race effect” (ORE)—the human advantage for identifying own- vs. other-race faces—exacerbates morph attack susceptibility for humans. We also asked whether face-identification performance in a deep convolutional neural network (DCNN) is affected by the race of morphed faces. Caucasian (CA) and East-Asian (EA) participants performed a face-identity matching task on pairs of CA and EA face images in two conditions. In the morph condition, different-identity pairs consisted of an image of identity “A” and a 50/50 morph between images of identity “A” and “B”. In the baseline condition, morphs of different identities never appeared. As expected, morphs were identified mistakenly more often than original face images. Of primary interest, morph identification was substantially worse for cross-race faces than for own-race faces. Similar to humans, the DCNN performed more accurately for original face images than for morphed image pairs. Notably, the deep network proved substantially more accurate than humans in both cases. The results point to the possibility that DCNNs might be useful for improving face identification accuracy when morphed faces are presented. They also indicate the significance of the race of a face in morph attack susceptibility in applied settings.