  We considered the Tsallis holographic dark energy model in frames of
Nojiri-Odintsov gravity with $f(R)=R+\lambda R^2-\sigma{\mu}/{R}$. For IR
cutoff event horizon is taken. The cosmological evolution of such universe is
investigated for various initial conditions and values of parameters. The
dependence of the Hubble parameter $H$ from time in the future has an
oscillations. It is shown that for $\mu \neq 0$ appearance of singularities are
typical and the time up to these singularities can be relatively small from
cosmological viewpoint. The singularity is associated with the zero of second
deribative of $f(R)$ on $R$. It is interesting to note that these models can
describe observational data from Ia supernovae astrophysics and dependence of
the Hubble parameter from redshift $z$ at least not worse than canonical
$\Lambda$CDM model.
