The Circular Electron Positron Collider (CEPC) is a future Higgs factory proposed by the Chinese high energy physics community. It will operate at a center-of-mass energy of 240-250 GeV. The CEPC will accumulate an integrated luminosity of 5 ab$^{rm{-1}}$ in ten years operation, producing one million Higgs bosons via the Higgsstrahlung and vector boson fusion processes. This sample allows a percent or even sub-percent level determination of the Higgs boson couplings. With GEANT4-based full simulation and dedicated fast simulation tool, we evaluated the statistical precisions of the Higgstrahlung cross section $sigma_{ZH}$ and the Higgs mass $m_{H}$ measurement at the CEPC in the $Zrightarrowmu^+mu^-$ channel. The statistical precision of $sigma_{ZH}$ ($m_{H}$) measurement could reach 0.97% (6.9 MeV) in the model-independent analysis which uses only the information of Z boson decay. For the standard model Higgs boson, the $m_{H}$ precision could be improved to 5.4 MeV by including the information of Higgs decays. Impact of the TPC size to these measurements is investigated. In addition, we studied the prospect of measuring the Higgs boson decaying into invisible final states at the CEPC. With the standard model $ZH$ production rate, the upper limit of ${cal B}(Hrightarrow rm{inv.})$ could reach 1.2% at 95% confidence level.
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