The features of the asynchronous correlation between accident indices and the factors that influence accidents can provide an effective reference for warnings of coal mining accidents. However, what are the features of this correlation? To answer this question, data from the China coal price index and the number of deaths from coal mining accidents were selected as the sample data. The fluctuation modes of the asynchronous correlation between the two data sets were defined according to the asynchronous correlation coefficients, symbolization, and sliding windows. We then built several directed and weighted network models, within which the fluctuation modes and the transformations between modes were represented by nodes and edges. Then, the features of the asynchronous correlation between these two variables could be studied from a perspective of network topology. We found that the correlation between the price index and the accidental deaths was asynchronous and fluctuating. Certain aspects, such as the key fluctuation modes, the subgroups characteristics, the transmission medium, the periodicity and transmission path length in the network, were analyzed by using complex network theory, analytical methods and spectral analysis method. These results provide a scientific reference for generating warnings for coal mining accidents based on economic indices.