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Strong gravitational lensing provides a natural opportunity to test GeneralRelativity (GR). We propose a model-independent method for simultaneousconstraining on Hubble constant ($H_0$) and post-Newtonian parameter(${\gamma_{\rm{PPN}}}$) using strong lensing systems and observational SNe Ia.The time-delay measurements from strong lesning can directly determine theHubble constant, and the lens distance inferred from the spectroscopicmeasurement of the stellar kinematics of the deflector galaxy can help us toconstrain the post-Newtonian parameter. We seek the Pantheon dataset andreconstruct unanchored distances using Gaussian process regression to achievethe cosmological model-independent GR testing instead of assuming a specificmodel, which can reduce possible bias on GR testing and measurement of Hubbleconstant. Combining the reconstructed unanchored distances and the four H0LiCOWlenses datasets, our results are $H_0=72.9^{+2.0}_{-2.3}{\mathrm{~km~s^{-1}~Mpc^{-1}}}$ and ${\gamma_{\rm{PPN}}}=0.89^{+0.17}_{-0.15}$.All the lenses show that there is no obvious evidence to support GR deviationwithin observational uncertainties. In the subsequent analysis, we consider aratio of distance ${D_{\Delta t}}/{D^{'}_{d}}$ method to further avoid theinfluence of $H_0$ on GR testing. The results show that, except J1206 withinthe $\sim1.2\sigma$ observational uncertainty, the remaining 3 lenses supportGR holds within the $1\sigma$ observational uncertainties.

Determining cosmological-model-independent $H_0$ and post-Newtonian parameter with time-delay lenses and supernovae