Genetic modifications in noncoding regulatory regions are likely critical to human evolution. Human-accelerated noncoding elements are highly conserved noncoding regions among vertebrates but have large differences across humans, which implies human-specific regulatory potential. In this study, we found that human-accelerated noncoding elements were frequently coupled with DNase I hypersensitive sites (DHSs), together with monomethylated and trimethylated histone H3 lysine 4, which are active regulatory markers. This coupling was particularly pronounced in fetal brains relative to adult brains, non-brain fetal tissues, and embryonic stem cells. However, fetal brain DHSs were also specifically enriched in deeply conserved sequences, implying coexistence of universal maintenance and human-specific fitness in human brain development. We assessed whether this coexisting pattern was a general one by quantitatively measuring evolutionary rates of DHSs. As a result, fetal brain DHSs showed a mixed but distinct signature of regional conservation and outlier point acceleration as compared to other DHSs. This finding suggests that brain developmental sequences are selectively constrained in general, whereas specific nucleotides are under positive selection or constraint relaxation simultaneously. Hence, we hypothesize that human- or primate-specific changes to universally conserved regulatory codes of brain development may drive the accelerated, and most likely adaptive, evolution of the regulatory network of the human brain.