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In this paper, we carry out a systematic study of the prospect of testinggeneral relativity with the inspiral signals of black hole binaries that couldbe detected with TianQin. The study is based on the parameterizedpost-Einsteinian (ppE) waveform, so that many modified gravity theories can becovered simultaneously. We consider black hole binaries with total massesranging from $10\rm M_\odot\sim10^7 M_\odot$ and ppE corrections atpost-Newtonian (PN) orders ranging from $-4$PN to $2$PN. Compared to thecurrent ground-based detectors, TianQin can improve the constraints on the ppEphase parameter $\beta$ by orders of magnitude. For example, the improvement atthe $-4$PN and $2$PN orders can be about $13$ and $3$ orders of magnitude(compared to the results from GW150914), respectively. Compared to futureground-based detectors, such as ET, TianQin is expected to be superior belowthe $-1$PN order, and for corrections above the $-0.5$PN order, TianQin isstill competitive near the large mass end of the low mass range $[10 \rmM_\odot, \,10^3 \rm M_\odot]\,$. Compared to the future space-based detectorLISA, TianQin can be competitive in the lower mass end as the PN order isincreased. For example, at the $-4$PN order, LISA is always superior forsources more massive than about $30\rm M_\odot\,$, while at the $2$PN order,TianQin becomes competitive for sources less massive than about $10^4\rmM_\odot$. We also study the scientific potentials of detector networksinvolving TianQin, LISA and ET, and discuss the constraints on specifictheories such as the dynamic Chern-Simons theory and the Einstein-dilatonGauss-Bonnet theory.

Testing general relativity with TianQin: the prospect of using the inspiral signals of black hole binaries