An intriguing magnetodielectric (MD) behavior is observed in geometrically frustrated spin-tetrahedral systems Cu2Te2O5X2 (X = Cl and Br). While the phase transition observed in the Cl-system at TN=18.5 K is consistent with 3D antiferromagnetic ordering, the phase transition at To=11.5 K in the Br-system has several unusual features. Concomitantly, a pronounced ferroelectric ordering is observed coinciding with TN of Cl-system and To of Br-system. At the highest applied magnetic field 90 kOe, the temperature dependent dielectric behavior with almost frequency independent well defined at TN~18.5 K are decrease compared with that at zero field for Cl-system, and at the highest applied magnetic field 90 kOe, the temperature dependent dielectric behavior with almost frequency independent well defined at Tm~30 K are decrease compared with that at zero field for Br-system. The ferroelectricity is ascribed to the polarization of the Te4+ lone-pair electrons, while the MD effect is argued to be due to exchange interaction involving frustrated tetramer clusters and intercluster exchange bridges.