The Doppler tracking data of the Chang'e 3 lunar mission is used to constrainthe stochastic background of gravitational wave in cosmology within the 1 mHzto 0.05 Hz frequency band. Our result improves on the upper bound on the energydensity of the stochastic background of gravitational wave in the 0.02 Hz to0.05 Hz band obtained by the Apollo missions, with the improvement reachingalmost one order of magnitude at around 0.05 Hz. Detailed noise analysis of theDoppler tracking data is also presented, with the prospect that these noisesources will be mitigated in future Chinese deep space missions. A feasibilitystudy is also undertaken to understand the scientific capability of the Chang'e4 mission, due to be launched in 2018, in relation to the stochasticgravitational wave background around 0.01 Hz. The study indicates that theupper bound on the energy density may be further improved by another order ofmagnitude from the Chang'e 3 mission, which will fill the gap in the frequencyband from 0.02 Hz to 0.1 Hz in the foreseeable future.
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