We establish a double noncommutative Jackiw-Teitelboim (JT) gravity model in 1+1 dimensions, which extends the results of Cacciatori et al. (Class. Quant. Grav. 19 (2002) 4029) by means of the double complex function theory. Not only can the two cases of the cosmological constant λ＞ 0 and λ＜ 0 be discussed in a unified way,but also the double solutions of this model, I.e. The de Sitter (dS2) and anti-de Sitter (AdS2) fuzzy spheres, can be derived simultaneously. Hence the results of Cacciatori et al. Are included as a special case.