Gag synthesis from the full-length unspliced mRNA is critical for the production of the viral progeny during human immunodeficiency virus type-1 (HIV-1) replication. While most spliced mRNAs follow the canonical gene expression pathway in which the recruitment of the nuclear cap-binding complex (CBC) and the exon junction complex (EJC) largely stimulates the rates of nuclear export and translation, the unspliced mRNA relies on the viral protein Rev to reach the cytoplasm and recruit the host translational machinery. Here, we confirm that Rev ensures high levels of Gag synthesis by driving nuclear export and translation of the unspliced mRNA. These functions of Rev are supported by the CBC subunit CBP80, which binds Rev and the unspliced mRNA in the nucleus and the cytoplasm. We also demonstrate that Rev interacts with the DEAD-box RNA helicase eIF4AI, which translocates to the nucleus and cooperates with the viral protein to promote Gag synthesis. Finally, we show that the Rev/RRE axis is important for the assembly of a CBP80-eIF4AI complex onto the unspliced mRNA. Together, our results provide further evidence towards the understanding of the molecular mechanisms by which Rev drives Gag synthesis from the unspliced mRNA during HIV-1 replication.