A new approach to study the indefinite stochastic linear-quadratic (LQ) optimal control problems called the “equivalent cost functional method” is introduced. Our analysis is featured by the introduction of some equivalent cost functionals which enable us to establish a bridge between the indefinite and positive-definite stochastic LQ problems. With such bridge, the solvability of the indefinite Hamiltonian system and Riccati equation are obtained. Consequently, the unique optimal control of the corresponding indefinite LQ problem is derived in the open-loop form via the solution of the Hamiltonian system, and also in terms of state feedback via the solution of the Riccati equation.