In this talk, we will present some recent results for time-inconsistent stochastic optimal control problems with all the coefficients being deterministic. Under certain conditions, we will derive the so-called equilibrium HJB equation for the equilibrium value function via which a time-consistent equilibrium control can be constructed, in principle. The well-posedness of such kind of HJB equation will be established for some special cases. The linear-quadratic situation and a generalized Merton portfolio problem will be carefully investigated.