Solid solution BiFe1-xCoxO3 shows anti-ferromagnetic order and pyroelectric order, simultaneously. It has been known that BiFe1-xCoxO3 exhibits a structural phase transition between monoclinic and tetragonal phases as x increases. This kinds of transition is often called morphotoropic phase boundary, which is well known to take place in a representative piezoelectric oxide, PbZr1-xTixO3. In order to theoretically understand the piezoelectric property in BiFe1-xCoxO3, we performed ab-initio electronic-structure calculations and studied the structural stability, the magnetic property, and the electronic polarization by means of super-cell approach. It turns out that the large electric polarization and the particular pyramidal coordination suppress the response of the electric polarization under strain. A way to enhance the piezoelectric effect in BiFe1-xCoxO3 is proposed.