We report the effective slowing and trapping of Cs atoms in an ultrahigh-vacuum apparatus. The heated Cs atoms in an oven are slowed using a Zeeman slower after the oven chamber and then trapped using a magneto-optical trap in a science chamber. Compared to the traditional vacuum pressure of ~10^-7 Pa determined by the vapor pressure of Cs atoms in the oven chamber, the designed cold nipple and differential pumping tube are used between the oven and the oven chamber to achieve a lower vacuum pressure of ~3.6×10^-9 Pa. This is beneficial for achieving and maintaining an ultrahigh vacuum in the science chamber. We demonstrate the performance of our apparatus through the effective slowing of Cs atoms and an optimal magneto-optical trap.