When H is a bipartite graph,the least signless Laplacian eigenvalue(the least Q-eigenvalue)of a class of graphs constructed by H was studied.It was shown that the sharp upper bound of the least Q-eigenvalue of the class of graphs is 1.Moreover,two necessary conditions were given for the graphs whose least Q-eigenvalue is equal to 1,and a class of graphs was constructed which have eigenvalue 1 as their least Q-eigenvalue.Also,a method was presented for checking a graph H without a perfect matching by using the least Q-eigenvalue of H∨K₁,and a sufficient condition was given when adding edges without changing the least Q-eigenvalue.At last,a class of graphs were constructed which have least Q-eigenvalue t,where t is a given positive integer.