Let \(Q(G)=D(G)+A(G)\) denote the signless Laplacian matrix (or Q(G)-matrix) of the graph G. Denote by q(G) (or Q(G)-index) the signless Laplacian spectral radius of the graph G. Let \(\theta (l_{1},l_{2},l_{3})\) denote the theta graph which consists of two vertices connected by three internally disjoint paths with length \(l_{1}\) , \(l_{2}\) and \(l_{3}\) . For odd \(n\ge 5\) , \(F_{n}\) denotes the graph consisting of \(\frac{n-1}{2}\) triangles which intersect in exactly one common vertex. For even \(n\ge 6\) , \(F_{n}\) denotes the graph obtained by hanging an edge to the maximal degree vertex of \(F_{n-1}\) . In this paper, we firstly show that if G is a \(\{C_{3},C_{4}\}\) -free graph with order \(n\ge 5\) and minimum degree \(\delta \ge 2\) , then \(q(G)\le \frac{n+3}{2}\) , unless \(G\cong C_{5}\) . Secondly, we show that if G is a \(\{\theta (1,2,2),F_{5}\}\) -free graph with order \(n\ge 6\) and minimum degree \(\delta \ge 2\) , then \(q(G)\le n\) , unless \(G\cong G_{3}\) for \(n=6\) or \(G\cong K_{t,n-t}\) for \(n\ge 6\) and \(2\le t\le n-2\) . Finally, we show that if G is a \(\{\theta (1,2,2),\theta (1,2,3)\}\) -free graph with size \(m\ge 9\) and minimum degree \(\delta \ge 2\) , then \(q(G)\le q(F_{\frac{2m+3}{3}})\) for \(m=3k, k\ge 3\) , unless \(G\cong F_{\frac{2m+3}{3}}\) .
