The global well-posedness of the damped Benjamin-Bona-Mahony equation is investigated in the \(L^{p}\) -based Sobolev space class \(\dot{H}^{s,p}({\mathbb {T}}^{3}).\) Firstly, using bilinear estimates and contraction mapping principle, the local well-posedness of the equation is originally shown in \(\dot{H}^{s,p}({\mathbb {T}}^{3})\) with \(s \ge \max \{0,\frac{3}{p}-1\}\) and \(\frac{3}{2}\le p<\infty .\) Secondly, using high-low frequency decomposition and Sobolev embedding, the global well-posedness of the damped Benjamin–Bona–Mahony is furthermore studied in \(\dot{H}^{s,p}({\mathbb {T}}^{3})\) with \( \max \{0,\frac{3}{p}-1\}\le s\le 1\) and \(\frac{3}{2}\le p\le 2\) .
