A least-squares finite element method for upper-convected Maxwell flow is proposed.The constitutive equation of a steady-state incompressible creeping model is linearized by using the approximations of velocity and stress.Least-squares functional involve the L²-norm of the residuals of each equation multiplied by a proper weight.The problem is transformed into minimize this functional.Euler-Lagrange equation corresponding to the least-squares functional is used to obtain the iterative equation.Finally this equation is solved by finite element method.