When a piezoelectric material is used as a sensor, the matrix is most likely to be a non-piezoelectric material. A piezoelectric ellipsoidal inhomogeneity embedded in a non-piezoelectric elastic matrix is analyzed via equivalent inclusion method in the present paper. Under this configuration the formulation of the inhomogeneity problem can be partially decoupled into an elastic problem and a dielectric inhomogeneity problem connected via some eigenstrain and "eigen-electricfield". A closed-form solution is obtained, which clearly shows the effects of piezoelectric properties on the sensitivity of the sensor. Although a generalized inhomogeneity problem of piezoelectric material has been considered by Wang (Int. J. Solids Structures29, 293 (1992) ), the general anisotropy of the material and the electro-mechanical coupling limited his formulation to reveal more insight conclusions. The direct application of this configuration as a sensor makes the present study important practically as well as theoretically.