Abstract: According to the foundational properties of the random errors, this paper deduces a more general error distribution---the unsymmetrical P-norm distribution, and then discusses the maximum likelihood adjustment of the p-norm distribution in detail. The distributions of degenerate、Laplace、normal and rectangular are the specific cases of the unsymmetrical P-norm distribution respectively. The maximum likelihood adjustment method of the unsymmetrical P-norm distribution is proposed, and the foundational equations of the adjustment are given. For each concrete measuring data, we can select a suitable value to be more close to the real one of the error than the normal distribution is. The method is the further generalization of the one of maximum likelihood adjustment of the P-norm distribution.