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A new simple dynamo model for stellar activity cycle is proposed. Byconsidering an inhomogeneous mean flow effect on turbulence, it is shown thatturbulent cross helicity (velocity--magnetic-field correlation) should enterthe expression of turbulent electromotive force as the coupling coefficient forthe mean absolute vorticity. The inclusion of the cross-helicity effect makesthe present model different from the current $\alpha$--$\Omega$-type modelsmainly in two points. First, in addition to the usual $\alpha$ (helicityeffect) and $\beta$ (turbulent magnetic diffusivity), we consider the $\gamma$coefficient (cross-helicity effect) as a key ingredient of the dynamo process.Second, unlike the $\alpha$ and $\beta$ coefficients, which are often treatedas an adjustable parameter in the current studies, the spatiotemporal evolutionof $\gamma$ coefficient is solved simultaneously with the mean magnetic-fieldequations. The basic scenario is as follows: In the presence of turbulent crosshelicity, the toroidal field is induced by the toroidal rotation in mediationby the turbulent cross helicity. The $\alpha$ effect generates the poloidalfield from the toroidal one. This poloidal field produces a turbulent crosshelicity whose sign is opposite to the original one. Then a cycle of reversalcompletes. Eigenvalue analyses of the simplest possible present model give abutterfly diagram, which confirms the above scenario as well as theequator-ward migrations, the phase relationship between the cross helicity andmagnetic fields, etc. These results suggest that the oscillation of theturbulent cross helicity is a key for the activity cycle. The reversal of theturbulent cross helicity is not the result of the magnetic-field reversal, butthe cause of the latter. This new model is expected to open up the possibilityof the mean-field or turbulence closure dynamo approaches.