It is well known that Approximated Maximum Likelihood(AML) estimator has the best performance for short time sampling wideband source bearing estimation. But for a long time, the heavy computational load of maximizing the multivariate, highly non-linear likelihood function prevented it from popular use. In this paper, we introduced Ant Colony Algorithm (ACA) to work with AML for computing the exact solutions to the likelihood function with a guarantee of global convergence. The resulted estimator is called Approximated Maximum Likelihood bearing estimator based on Ant Colony Algorithm (ACA-AML). Simulations show that ACA-AML not only reduces the computational complexity greatly but also maintains the excellent performance of the original AML estimator.