The coronal magnetic configuration behind coronal mass ejections (CMEs) can commonly be stretched severely, thus to push the magnetic fields with opposite polarities to approach each other, and to form a current sheet of magnetic reconnection. The current sheet in solar eruptions is not only an important region to convert the magnetic free energy into thermal energy, plasma kinetic energy, and energetic particle beams, but also plays a role to connect CMEs and flares. In the CME events of 2003 January 3 and 2003 November 4, the development of current sheet has been observed in both cases. We have investigated the dynamic features and physical properties of current sheet in the two events, based on the data of LASCO (Large Angle and Spectrometric Coronagraph) and UVCS (Ultraviolet Coronagraph Spectrometer) on board of SOHO (Solar and Heliospheric Observatory), and the Hα data from BBSO (Big Bear Solar Observatory) and YNAO (Yunnan Astronomical Observatory). The existence of ions with a high degree of ionization, such as Fe+17 and Si+11, indicates a high temperature up to 3×106 ∼5×106 K in the region of current sheet. A direct measurement shows that the thickness of current sheet varies between 1.3×104 and 1.1×105 km, which increases first and then decreases with time. Using the CHIANTI code (v.7.1), we have further calculated the average values of electron temperature and corresponding emission measure (EM) respectively to be 3.86×106 K and 6.1×1024 cm-5 in the current sheet of the 2003 January 3 event. We also find that the current sheet twisted forth and back quasi-periodically during the eruption event on 2003 November 4 by analyzing the observational data from SOHO/UVCS.