  In 2017, LHCb collaboration reported their first observation of the rare
decays $B_s \to \phi (f_0(980)$ $/f_2(1270) \to ) \pi^+\pi^-$ and the evidence
of $B^0 \to \phi(f_0(980)/f_2(1270)\to)\pi^+\pi^-$. Motivated by this, we study
these quasi-two-body decays in the perturbative QCD approach. The branching
fractions, $CP$ asymmetries and the polarization fractions are calculated. We
find that within the appropriate two-meson wave functions, the calculated
branching fractions are in agreement with the measurements of LHCb. Based on
the narrow-width approximation, We also calculate the branching fractions of
the quasi-two-body $B_{d,s}\to \phi(f_0(980)/f_2(1270)\to) \pi^0\pi^0$ and
$B_{d,s}\to \phi(f_2(1270)\to) K^+K^-$, and hope the predictions to be tested
in the ongoing LHCb and Belle II experiments. Moreover, the processes
$B_{d,s}\to \phi f_2(1270)$ are also analyzed under this approximation. We note
that the $CP$ asymmetries of these decays are very small, because these decays
are either penguin dominant or pure penguin processes.
