A　book　Bn　${B}_{n}$　is　a　graph　which　consists　of　n　$n$　triangles　sharing　a　common　edge.　In　1978,　Rousseau　and　Sheehan　conjectured　that　the　Ramsey　number　satisfies　r(Bm,Bn)＜=　2(m+n)+c　$r({B}_{m},{B}_{n})\le　\,2(m+n)+c$　for　some　constant　c＞0　$c\gt　0$.　In　this　article,　we　obtain　that　r(Bm,Bn)＜=　2(m+n)+o(n)　$r({B}_{m},{B}_{n})\le　2(m+n)+o(n)$　for　all　m　＜=　n　$m\le　n$　and　n　$n$　large,　which　confirms　the　conjecture　of　Rousseau　and　Sheehan　asymptotically.　As　a　corollary,　our　result　implies　that　a　related　conjecture　of　Faudree,　Rousseau　and　Sheehan　on　strongly　regular　graph　holds　asymptotically.