  New tests are proposed to constrain possible deviations from local Lorentz
invariance and local position invariance in the gravity sector. By using
precise timing results of two binary pulsars, i.e., PSRs J1012+5307 and
J1738+0333, we are able to constrain (strong-field) parametrized post-Newtonian
parameters $\hat{\alpha}_1$, $\hat{\alpha}_2$, $\hat{\xi}$ to high precision,
among which, $|\hat{\xi}| < 3.1\times10^{-4}$ (95% C.L.) is reported here for
the first time.
