Left-right asymmetry is subtle but pervasive in the human central nervous system. This asymmetry is initiated early during development, but its mechanisms are poorly known. Forebrains and midbrains were dissected from six human embryos at Carnegie stages 15 or 16, one of which was female. The structures were divided into left and right sides, and RNA was isolated. RNA was sequenced with 100 base-pair paired ends using Illumina Hiseq 4000. After quality control, five paired brain sides were available for midbrain and forebrain. A paired analysis between left- and right sides of a given brain structure across the embryos identified left-right differences. The dataset, consisting of Fastq files and a read count table, can be further used to study early development of the human brain