A single-layer cylindrical reticulated shell was taken as an example to study the dynamic instability of spatial structures by the Budiansky-Roth criterion. The Budiansky-Roth criterion was explained and the wind tunnel test of the single-layer cylindrical reticulated shell was conducted to obtain the fluctuating wind loads on it. Then, its dynamic instability under fluctuating wind loads was studied, in which the influence of initial geometrical imperfections, wind directions and coefficients of wind pressure were discussed and comparisons with stability analysis results from the Chinese standard and the gust response factor (GRF) method were made. The results show that study on the dynamic instability of spatial structures under fluctuating wind loads is necessary.