  In this paper, we study the quasi-two-body decays $B\to P f_0(500)\to
P\pi^+\pi^-$ (with $P=(\pi, K, \eta, \eta^{\prime})$) within framework of
perturbative QCD (PQCD) factorization approach. With the help of $\pi$-$\pi$
distribution amplitude and scalar form factor $F_{\pi\pi}(\omega^2)$, we
calculate the CP averaged branching fraction and the CP asymmetry for the
quasi-two-body decays $B\to P f_0(500)\to P\pi^+\pi^-$. Taking the
quasi-two-body decay $B^+ \to \pi^+ f_0(500) \to \pi^+ \pi^+ \pi^-$ as an
explicit example, we present the behaviour of differential branching fraction
and direct CP violation versus the $\pi$-$\pi$ invariant mass. The total
branching fraction and direct CP violation are $\mathcal{B}(B^+\to \pi^+
[\sigma\to]\pi^+\pi^-) = (1.78 \pm 0.41\pm 0.51) \times 10^{-6}$ and
$\mathcal{A}_{\rm CP}(B^+\to \pi^+ [\sigma\to]\pi^+\pi^-) = (29.8\pm 11.1\pm
13.0)\%$ respectively. Our results could be tested by further experiments.
