The diffraction of Lamb waves by a finite delamination situated on a random plane parallel to the symmetric plane of a laminated plate is taken into account. Two imaginary planes are introduced to solve the problem by adopting the method of mode matching. By taking an appropriate finite number of terms of the infinite expansion series and some selected points on the two imaginary planes through convergence and precision tests, a matrix equation is obtained to evaluate the expansion coefficients numerically. Reflection coefficients versus the normalized length a/h and the relative location h1/h of the delamination are calculated in the low-frequency domain, the relative errors are found to be less than 1%. Results obtained indicate that the theory developed in this paper is meaningful for the detection of both the size and the location of a delamination in a laminated plate by cooperating with experimental techniques for the non-destructive evaluation (NDE) technology.