Cranial Neural Crest Cells (CNCC) originate at the cephalic region from forebrain, midbrain and hindbrain, migrate into the developing craniofacial region, and subsequently differentiate into multiple cell types. The entire specification, delamination, migration, and differentiation process is highly regulated and abnormalities during this craniofacial development cause birth defects. To better understand the molecular networks underlying CNCC, we integrate paired gene expression & chromatin accessibility data and reconstruct the genome-wide human Regulatory network of CNCC (hReg-CNCC). Consensus optimization predicts high-quality regulations and reveals the architecture of upstream, core, and downstream transcription factors that are associated with functions of neural plate border, specification, and migration. hReg-CNCC allows us to annotate genetic variants of human facial GWAS and disease traits with associated cis-regulatory modules, transcription factors, and target genes. For example, we reveal the distal and combinatorial regulation of multiple SNPs to core TF ALX1 and associations to facial distances and cranial rare disease. In addition, hReg-CNCC connects the DNA sequence differences in evolution, such as ultra-conserved elements and human accelerated regions, with gene expression and phenotype. hReg-CNCC provides a valuable resource to interpret genetic variants as early as gastrulation during embryonic development. The network resources are available at https://github.com/AMSSwanglab/hReg-CNCC .