It is known that the stochastic gradient descent (SGD)-based constant modulus algorithm (CMA) has the drawback of slow convergence rate. It is also known that under some weak conditions, all local minima of CMA are identical to that of a CMA which is constrained in signal subspace. Based on this property, we propose a subspace-constrained CMA that is able to increase the convergence rate of the conventional SGD-CMA. To reduce the computational complexity, a technique referred to as projection approximate subspace tracking with deflation (PASTd) is used to calculate the signal subspace. Our simulation shows that the proposed algorithm is significantly superior to the conventional SGD-CMA both in the convergence rate and in the sensitivity to the step size.