The effect of electric fields on the dielectric properties of charge-ordered La1-xCaxMnO3 compounds is reported. A low-frequency giant dielectric tunability can be obtained under a bias field as low as of the order of similar to 10 V/cm. The analyses suggest that the giant dielectric tunability under low bias fields could be derived from the extrinsic contributions such as intergrains and Schottky barriers. In addition, the tunability strongly depends on the stability of the charge-ordered state of the compounds. These findings make it possible to achieve a high tunability of nonferroelectrics in low electric fields, indicating that it is promising for potential applications, such as tunable devices.