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The photodetachment dynamics of H-ion in a harmonic potential plus an oscillating electric field is studied using the time-dependent closed orbit theory.An analytical formula for calculating the photodetachment cross section of this system is put forward.It is found that the photodetachment cross section of this system is nearly unaffected for the weak oscillating electric field strength,but oscillates complicatedly when the oscillating electric field strength tus strong.In addition,the frequency of the harmonic potential and the oscillating electric field (the frequency of the harmonic potential and the frequency of the oscillating electric field are the same in the paper,unless otherwise stated.) can also affect the photodetachment dynamics of this system.With the increase of the frequency in the harmonic potential and the oscillating electric field,the number of the closed orbits for the detached electrons increased,which makes the oscillatory structure in the photodetachment cross section much more complex.Our study presents an intuitive understanding of the photodetachment dynamics driven by a harmonic potential plus an oscillating electric field from a space and time dependent viewpoint.This study is very useful in guiding the future experimental research for the photodetachment dynamics in the electric field both changing with space and time.