A forward-propagation learning rule (FPL) has been proposed for acquiring neural inverse models without back-propagated signals based on a Newton-like method. A modified multiple linear regression, RLS algorithms or a Fisher's scoring method have been applied to the FPL, although these methods does not necessarily achieve goal-directed learning. In the current work, to guarantee goal-directed learning, a modified method for FPL is derived as one of gradient methods in terms of maximum likelihood estimation. The forward-propagated errors on the learning model and the covariance matrices are evaluated to calculate the gradients which are used in the proposed method. The suitability of the proposed method is confirmed by computer simulation in motor learning.