We are concerned with the existence of positive solutions of singular second-order boundary value problem u″(t)+f(t,u(t))=0, t∈(0,1), u(0)=u(1)=0, which is not necessarily linearizable. Here, nonlinearity f is allowed to have singularities at t=0,1. The proof of our main result is based upon topological degree theory and global bifurcation techniques.