In this paper, the global exponential stability for recurrent neural networks (QVNNs) with asynchronoustime delays is investigated in quaternion field. Due to the non-commutativity of quaternion multiplicationresulting from Hamilton rules: ij = −ji = k, jk = −kj = i, ki = −ik = j, ijk = i2= j2= k2= −1,the QVNN is decomposed into four real-valued systems, which are studied separately. The exponentialconvergence is proved directly accompanied with the existence and uniqueness of the equilibrium pointto the consider systems. Combining with the generalized ∞-norm and Cauchy convergence property inthe quaternion field, some sufficient conditions to guarantee the stability are established without usingany Lyapunov–Krasovskii functional and linear matrix inequality. Finally, a numerical example is givento demonstrate the effectiveness of the results.