Motivated by the observations of the decays B^0 rightarrow K_0^{*}(1430)^0 f_0(980) and B^0 rightarrow K_2^{*}(1430)^0 f_0(980) from BaBar collaboration, we study the B^{0(+)} rightarrow K_{0,2}^{*}(1430)^{0(+)} f_0(980)/sigma decays in the perturbative QCD approach for the first time. In the absence of reliable nonperturbative wave functions we only assume the scalar meson f_0(980) and sigma are two-quark ground states. In our calculations, these decays are all dominated by the hard-scattering emission and annihilation diagrams, while the factorizable emission diagrams are forbidden or suppressed heavily by the vector decay constants. Furthermore, the branching fractions are sensitive to the mixing between f_0(980) and sigma . Comparing our results with the experimental data, a large mixing angle theta is favored. Taking theta =145^circ , the orders of branching fractions of B rightarrow K_0^{*}(1430)^0 sigma , B rightarrow K_{2}^{*}(1430)^0 sigma and B rightarrow K_{0,2}^{*}(1430)^0 f_0(980) are predicted to be 10^{-4}, 10^{-5} and 10^{-6}, respectively, which can be measured in the current experiments such as LHCb and Belle-2. In addition, although these decays are penguin dominant, the mixing also leads to large direct CP asymmetries in these decays. With the precise data in future, our results could shed light on the inner structure of the scalar mesons and can be used to determine the mixing angle of the sigma -f_0(980) system.