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Motivated by empirical evidence for rough volatility models, this paperinvestigates continuous-time mean-variance (MV) portfolio selection under theVolterra Heston model. Due to the non-Markovian and non-semimartingale natureof the model, classic stochastic optimal control frameworks are not directlyapplicable to the associated optimization problem. By constructing an auxiliarystochastic process, we obtain the optimal investment strategy, which depends onthe solution to a Riccati-Volterra equation. The MV efficient frontier is shownto maintain a quadratic curve. Numerical studies show that both roughness andvolatility of volatility materially affect the optimal strategy.

Mean-variance portfolio selection under Volterra Heston model