Based on a sample of $2.25times 10^{8}$ $J/psi$ events collected with the BESIII detector at BEPCII, a full partial wave analysis on $J/psitogammaetaeta$ was performed using the relativistic covariant tensor amplitude method. The results show that the dominant $0^{++}$ and $2^{++}$ components are from the $f_0(1710)$, $f_0(2100)$, $f_0(1500)$, $f_2(1525)$, $f_2(1810)$ and $f_2(2340)$. The resonance parameters and branching fractions are also presented.