We designed and synthesized a pseudo-binary Pb-free system, Ba(Ti0.7Zr0.3)O3-x(Ba0.82Ca0.18)TiO3, by combining a rhombohedral end (with only cubic to rhombohedral ferroelectric phase transition) and a tetragonal end (with only cubic to tetragonal ferroelectric phase transition). The established composition-temperature phase diagram is characterized by a tricritical point type morphotropic phase boundary (MPB), and the MPB composition has better ferroelectric, piezoelectric, and dielectric properties than the compositions deviating from MPB. Moreover, a full set of material constants (including elastic stiffness constants, elastic compliance constants, piezoelectric constants, dielectric constants, and electromechanical coupling factors) of the MPB composition are determined using a resonance method. The good piezoelectric performance of the MPB composition can be ascribed to the high dielectric constants, elastic softening, and large electromechanical coupling factor.