To better understand the decay of different types of sunspots, we studied the decay of eight alpha-configuration sunspots by using the data that were acquired by the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory. We followed their decay for about four days and analyzed the evolution of their photospheric area and magnetic field parameters. We found that the area and total magnetic flux of alpha sunspots show a near-linear decrease during their decay. Meanwhile, the area decay rate of an individual sunspot is not constant. The area decay of a sunspot can be divided into two stages, a slow and a rapid decay process. Moreover, according to the difference of the area decay of the penumbra and umbra, the alpha sunspots decay can be classified in three ways: the penumbra and umbra decay synchronously, the penumbra decays first, and the umbra decays first. In addition, the flux decay of the penumbra is lagging behind the decay of the penumbral area. This finding suggests that the vertical magnetic field of the sunspot penumbra increases significantly in the early stage of sunspot decay.