We report a study of a compound solar eruption that was associated with two consecutively erupting magnetic structures and correspondingly two distinct peaks, during impulsive phase, of an M-class flare (M8.5). Simultaneous multi-viewpoint observations from $textit{SDO}$, $textit{GOES}$ and $textit{STEREO-A}$ show that this compound eruption originated from two pre-existing sigmoidal magnetic structures lying along the same polarity inversion line. Observations of the associated pre-existing filaments further show that these magnetic structures are lying one on top of the other, separated by 12 Mm in height, in a so-called double-decker configuration. The high-lying magnetic structure became unstable and erupted first, appearing as an expanding hot channel seen at extreme ultraviolet wavelengths. About 12 minutes later, the low-lying structure also started to erupt and moved at an even faster speed compared to the high-lying one. As a result, the two erupting structures interacted and merged with each other, appearing as a single coronal mass ejection in the outer corona. We find that the double-decker configuration is likely caused by the persistent shearing motion and flux cancellation along the source active regions strong-gradient polarity inversion line. The successive destabilization of these two separate but closely spaced magnetic structures, possibly in the form of magnetic flux ropes, led to a compound solar eruption. The study of the compound eruption provides a unique opportunity to reveal the formation process, initiation, and evolution of complex eruptive structures in solar active regions.