In queueing theory, the Lorden's inequality can be used for bounds esimation of the moments of backward and forward renewal times. Two random variables called backward renewal time and forward renewal time for this process are defined. The Lorden's inequality it's true for renewal process, so expectations of backward and forward renewal times are bounded by the relation of expectation of moment of random variable for any fixed moment of time, where random variables are i.i.d. We generalised and proved a similar result for dependent random variables with finite expectations, some constant C and integrable function Q(s): if X are not independent and have absolutely continuous distribution function which satisfies some boundary conditions, then the analogue of Lorden's inequality for renewal process is true.