Provided is a method for beamforming by using maximum likelihood estimation in a speech recognition apparatus, including: (a) receiving an input signal (Xn,k) at a time frame n and a frequency k where noise is mixed: (b) determining a probability density function for a target signal (Yn,k) obtained by removing the noise from the input signal satisfies a complex generalized Guassian distribution or a complex gamma distribution where an average value is zero in a time-frequency domain; (c) estimating a variance (λn,k) of the target signal so as to maximize log likelihood for the probability density function; (d) estimating a filter (wk) maximizing a cost function so as to maximize the log likelihood for the probability density function; and (e) repeatedly performing the estimation of the steps (c) and (d) until the filter (wk) coverages, and finally acquiring a final filter (wk).