The experiments on the laser cooling and trapping of ytterbium atoms are reported, including the two-dimensional transversal cooling, longitudinal velocity Zeeman deceleration, and a magneto-optical trap with a broadband transition at a wavelength of 399 nm. The magnetic field distributions along the axis of a Zeeman slower were measured and in a good agreement with the calculated results. Cold ytterbium atoms were produced with a number of about 10⁷ and a temperature of a few milli-Kelvin. In addition, using a 556-nm laser, the excitations of cold ytterbium atoms at ¹S₀-³P₁ transition were observed. The ytterbium atoms will be further cooled in a 556-nm magneto-optical trap and loaded into a three-dimensional optical lattice to make an ytterbium optical clock.