We formulate the open-loop control framework for time-consistent mean-variance (TCMV) portfolio problems in incomplete markets with stochastic volatility (SV). We offer the existence and uniqueness results of the TCMV equilibrium controls for general SV models and derive explicit closed-form equilibrium controls for several popular models, including the Heston, Hull-White and 3/2 SV models. The uniqueness of the equilibrium controls are related to the mean-reverting speed of the volatility and the investment horizon. (C) 2019 Elsevier Ltd. All rights reserved.