The strong deviation theorem in probability theory is a natural extension of the classical strong law of large numbers. In this paper, we first introduce the concept of the asymptotic generalized logarithmic likelihood ratio as a random measure of deviation between the arbitrarily dependent array of random variables and an array of row-wise independent random variables. Using truncation technique for random variables, we construct likelihood ratio with one parameter and expectation of 1, then by applying of the Borel-Cantelli lemma, we derive almost everywhere convergence of random variables. Under some conditions of Chung type, we obtain the upper and lower bounds on the deviation between the partial sum of arbitrarily dependent array of random variables and the expectations of the random variable of the reference measure. And the upper and lower bounds are presented by the generalized relative entropy functions. It is worth noting that the proof of the theorem does not involve the complex measure theory, but only the simple pure analysis method. The results extend some existing conclusions and the applications of the strong limit theorem.