Hyperfine-structure (HFS) of atoms results from the interactions between the nuclear magnetic dipole moment and the magnetic field generated by the electrons (related to the magnetic dipole hyperfine constant Ahfs), and between the nuclear electric quadrupole moment and the electric field gradient due to the distribution of charge within atoms (related to the electric quadrupole hyperfine constant Bhfs), so the accurate measurement of HFS is of interest in many fields, including atomic parity nonconservation, tests of fundamental physics, electron-nucleus interaction, and high resolution spectrum and so on. Generally, in order to obtain the atomic spectra, the frequency of laser needs to be scanned over the hyperfine transitions of atoms, so the nonlinear effect from the laser frequency scanning often limits the measurement accuracy of hyperfine splitting. In this paper, we solve this problem, and demonstrate a novel method to measure the hyperfine splitting of atoms. Taking cesium (Cs) for example, based on the Cs 6S1/2-6P3/2-7S1/2 (852.3 nm + 1469.9 nm) ladder-type atomic system, three sets of optical-optical double resonance (OODR) spectra are obtained in a room-temperature vapor cell, when the 852.3 nm laser is tuned to the 6S1/2 (F=4)-6P3/2 (F'=4) resonant transition, and the carriers of 1469.9 nm probe laser accompanied with1 sidebands from a phase-type electro-optical modulator (EOM) are scanned over the whole 6P3/2-7S1/2 hyperfine transitions. Owing to the Doppler effect, some of the hyperfine transitions in these three sets of OODR spectra overlap with the narrowest linewidth only when the frequency of the signal driving EOM equals the value of hyperfine splitting 7S1/2 state. Using this phenomenon which can effectively avoid the nonlinear influence on the measurement during the frequency scanning process of 1469.9 nm laser, we measure the hyperfine splitting of 7S1/2 state to be (2183.720.23) MHz, and the magnetic dipole hyperfine constant Ahfs to be (545.930.06) MHz, which are consistent with previously reported experimental results. This technique provides a robust and simple method of measuring hyperfine splitting with a high precision, which is significant to provide the useful information about atomic structure for developing a more accurate theoretical model describing the interaction within an atom.