In this paper, we consider a class of singular equations depending on quadratic gradient term in the form ∂u/∂t-Δu=-μ|\nabla u|l/μm+f(x, t), (x, t)∈Ω×(0, T], with zero boundary and nonnegative initial conditions, where Ω is a bounded subset of RN with ∂Ω of C2 class, T>0 and μ>0, parameters 1<m+1≤l ≠ 2 or 0<m<l=2, the datum f and initial condition φ are both nonnegative functions satisfying some assumptions. We call problem -Δuμ |\nabla u|l/um+f(x) in Ω, u|∂Ω=0, is its stationary problem. First, we prove the existence and uniqueness of positive classical solutions of these two problems, denoted by u, v respectively. Secondly, under some assumptions, we prove limt→+∞u
=v is a positive classical solution of the stationary problems.