We develop a framework based on deep reinforce-ment learning (DRL) to solve the spectrum allocation problem inthe emerging integrated access and backhaul (IAB) architecturewith large scale deployment and dynamic environment. The avail-able spectrum is divided into several orthogonal sub-channels,and the donor base station (DBS) and all IAB nodes have thesame spectrum resource for allocation, where a DBS utilizes thosesub-channels for access links of associated user equipment (UE)as well as for backhaul links of associated IAB nodes, and anIAB node can utilize all for its associated UEs. This is one ofkey features in which 5G differs from traditional settings wherethe backhaul networks were designed independently from theaccess networks. With the goal of maximizing the sum log-rateof all UE groups, we formulate the spectrum allocation probleminto a mix-integer and non-linear programming. However, itis intractable to find an optimal solution especially when theIAB network is large and time-varying. To tackle this problem,we propose to use the latest DRL method by integrating anactor-critic spectrum allocation (ACSA) scheme and deep neuralnetwork (DNN) to achieve real-time spectrum allocation indifferent scenarios. The proposed methods are evaluated throughnumerical simulations and show promising results compared withsome baseline allocation policies.