We provide the first report on the harmonics generated by an intense femtosecond vector beam that is normally incident on a solid target. By using 2D particle-in-cell (PIC) codes, we observe the third and the fifth harmonic signals with the same vector structure as the driving beam, and obtain an attosecond vector beam pulse train. We also show that the conversion efficiencies of the third and the fifth harmonics reach their maxima for a plasma density of four times the critical density due to the plasma resonating with the driving force. This method provides a new means of generating intense extreme ultraviolet (XUV) vector beams via ultra-intense laser-driven harmonics.