The magnetoelectric coupling in the spin glass BaCo6Ti6O19 with the magnetoplumbite structure was examined. We have successfully grown single crystals of this compound and revealed the XY-like spin glass nature with a glass transition at T-g approximate to 14 K. It was found that the electric polarization P gradually develops below about 50K and shows a substantial anomaly at around T-g. Furthermore, the magnitude of P strongly depends on the magnetoelectric cooling condition below T-g and shows a memory effect coupled with the spin sector. The present result indicates that BaCo6Ti6O19 exhibits a magnetoelectric glass nature in which a frozen state of electric dipoles is coupled with that of magnetic ones and can be modulated magnetoelectrically.