In order to measure a weak alternating magnetic field, an optically-pumped Rb magnetometer based on pump-probe structure is investigated and demonstrated. The pumping light and probing light propagate along the z axis and x axis, respectively. A constant polarization magnetic field along the pumping light is applied, which not only stabilizes the polarization of Rb atoms but also tunes resonance frequency of Rb atoms. When a weak alternating magnetic field is applied perpendicularly to the constant magnetic field, the magnetic moment will tip off the z axis and rotate around the z axis. And then the polarization plane of probing light is modulated correspondingly. The x component of the magnetic moment can be obtained with a balanced detector. As a result, a signal proportional to weak alternating magnetic field can be obtained.In order to obtain the magnetic response of the magnetometer, we analyze the signal amplitude as a function of polarization magnetic field strength B0 and transverse relaxation time 2 with numerical simulation. The amplitude-frequency response of the magnetometer is determined mainly by two parameters, namely cutoff frequency c=1/2 and resonance frequency 0= B0, where is the gyromagnetic ratio of Rb atom. At low frequency, that is a0 and a 0c2, the magnetometer has a flat response, here a is the frequency of the weak alternating magnetic field. If 0c, the signal amplitude will be large for large 0 or small c. For a given c, the peak response appears at 0=c. In the vicinity of resonance frequency, if c0, a peak will appear and if c 0, no peak occurs. At high frequency, the amplitude will decrease with the increase of a.We verify the above analyses in experiment. A vapor cell with a short transverse relaxation time is used to obtain large frequency response bandwidth. Through optimizing the powers and frequencies of pumping laser and probing laser, high polarization and detection sensitivity of atomic spin can be obtained. Moreover, through choosing an appropriate polarization magnetic field, the magnetometer can be maximally sensitive to the magnetic field to be measured. The experimental results show that the magnetometer has a sensitivity of about m 0.2; pT/HzHz and bandwidth of about 3.5 kHz. It can be used to detect low field magnetic resonance and high frequency abnormal physical phenomena.