  The so-called hyperon puzzle in the theory of neutron stars is considered in
the framework of modified $f(R)$ gravity. We show that for simple hyperon
equations of state, it is possible to obtain the maximal neutron star mass
which satisfies the recent observational data for PSR J1614-2230, in
higher-derivative models with power-law terms as $f(R) = R+\alpha R^2+ \beta
R^3$. The soft hyperon equation of state under consideration is usually treated
as non-realistic in the standard General Relativity. The numerical analysis of
Mass-Radius relation for massive neutron stars with hyperon equation of state
in modified gravity turns out to be consistent with observations. Thus, we show
that the same modified gravity can solve at once three problems: consistent
description of the maximal mass of neutron star, realistic Mass-Radius relation
and account for hyperons in equation of state.
