A new type of internal signal stochastic resonance (ISSR) is found and investigated numerically by simulating a chemical model, which is proposed to account for chaos in the Belousov-Zhabotinsky reaction. When the system is in the dynamical region of period-1 oscillation, Gaussian white noise perturbation of the control parameter causes maxima to appear on the curve of signal-to-noise ratio versus noise intensity, showing the characteristic of stochastic resonance. The differences between this new type ISSR and the previous one studied by Hu et al. [Phys. Rev. Lett. 71, 807 (1993)] and Xin et al. [J. Chem. Phys. 111, 721 (1999)] are discussed.