In 2017, LHCb collaboration reported their first observation of the rare decays B_s rightarrow phi (f_0(980)/f_2(1270) rightarrow ) pi ^+pi ^- and the evidence of B^0 rightarrow phi (f_0(980)/f_2(1270)rightarrow )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}rightarrow phi (f_0(980)/f_2(1270)rightarrow ) pi ^0pi ^0 and B_{d,s}rightarrow phi (f_2(1270)rightarrow ) K^+K^-, and hope the predictions to be tested in the ongoing LHCb and Belle II experiments. Moreover, the processes B_{d,s}rightarrow phi f_2(1270) are also analyzed under the approximation. We note that the CP asymmetries of these decays are very small, because these decays are either penguin dominant or pure penguin processes.