The dynamics of spiral waves in a two-layer coupled excitable medium is studied by using the Bär-Eiswirth model. The two layers of medium are connected via network, i.e., a excitable unit is selected in each column of an excitable medium as a central point, and all excitable units in the same column of a layer medium are connected only with the corresponding central point and its eight neighbors in the opposite medium. The numerical results show that when the coupling strength is appropriately small, the two coupled spiral waves via local coupling can achieve their synchronization. Increasing coupling strength will induce meandering and drifting of spiral waves, leading to a desynchrony between the coupled spiral waves. The spiral wave with the resting state, low frequency plan wave and irregular pattern are observed to coexist. The coupled spiral waves via the transformation of spiral wave to synchronous plane wave disappear if the coupling strength is appropriately chosen. The physical mechanisms behind these phenomena are discussed.