In this paper we present the results of a statistical study of the accelerations of coronal mass ejections (CMEs). A CME usually undergoes a multiphased kinematic evolution, with a main acceleration phase characterized by a rapid increase of CME velocity in the inner corona, followed by a relatively smooth propagation phase characterized by a constant speed or a small residual acceleration in the outer corona. We study both the main acceleration and the residual acceleration for 50 CME events based on Large Angle Spectrometric Coronagraph (LASCO) observations. We find that the magnitude of the main acceleration has a wide distribution, from 2.8 to 4464.0 m s À2 , with a median (average) value of 170.1 (330.9 m s À2 ), and a standard deviation of 644.8 m s À2 , whereas the magnitude of the residual acceleration ranges only from À131.0 to 52.0 m s À2 , with a median (average) value of 3.1 (0.9 m s À2 ) and a standard deviation of 25.3 m s À2 . The duration of the main acceleration is also widely distributed, from 6 to 1200 minutes, with a median (average) value of 54 (180 minutes) and a standard deviation of 286 minutes.We find an intriguing scaling law between the acceleration magnitude (A) and the acceleration duration (T ) over the entire parameter range of almost 3 orders of magnitude, which can be expressed as A (m s À2 ) ¼ 10; 000T À1 (minutes). The implications of these observational results on the issues of CME classification and CME modelings are discussed.