We determine the maximal number of independent holomorphic functions on the Thurston manifolds $M^{2r+2}$, r ≥ 1, which are the first discovered compact non-Kähler almost Kähler manifolds. We follow the method which involves analyzing the torsion tensor dθ modθ, where $\theta =(\theta ¹,...,{\theta }^{r+1})$ are independent (1,0)-forms.