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We have successfully synthesized three quasi-2D geometrically frustrated magnetic compounds (\alpha-MCr_2O_4, M=Ca, Sr, Ba) using the spark-plasma-sintering technique. All these members of the \alpha-MCr_2O_4 family consist of the stacking planar triangular lattices of Cr$^{3+}$ spins (${\rm S}=3/2$), separated by non-magnetic alkaline earth ions. Their corresponding magnetic susceptibility, specific heat, dielectric permittivity and ferroelectric polarization are systematically investigated. A long-range magnetic ordering arises below the N\'{e}el temperature (around 40K) in each member of the \alpha-MCr_2O_4 family, which changes to the quasi-120\degree proper-screw-type helical spin structure at low temperature. A very small but confirmed spontaneous electric polarization emerges concomitantly with this magnetic ordering. The direction of electric polarization is found within the basal triangular plane. The multiferroicity in \alpha-MCr_2O_4 can not be explained within the frameworks of the magnetic exchange striction or the inverse Dzyaloshinskii-Moriya interaction. The observed results are more compatible with the newly proposed Arima mechanism that is associated the d-p hybridization between the ligand and transition metal ions, modified by the spin-orbit coupling. The evolution of multiferroic properties with the increasing inter-planar spacing (as M changes from Ca to Ba) reveals the importance of interlayer interaction in this new family of frustrated magnetic systems., Comment: 10 pages, 8 figures, published online in Physical Review B