In IEEE 802.11ax, orthogonal frequency division multiple access (OFDMA) is introduced in the uplink for multi-user transmission. The uplink resource units (RUs) can be allocated by the combination of random access (RA) and scheduled access (SA) with specific proportion. And the RU allocation ratio of RA to SA will affect the overall performance. In this paper, an adaptive uplink resource allocation scheme is proposed based on the analysis of access delay. To achieve minimum average delay, according to the distribution of different kinds of traffic and the number of stations (STAs) which have reserved RUs for the next uplink transmission, a specific proportion of RUs are allocated for SA and the remainders are for RA. The specific allocation of RUs is obtained by solving the objective function which aims to minimize the expected access delay. When the distribution of traffic or the number of reserved RUs changes, the allocation of RUs for SA and RA will be adjusted accordingly. In this manner, the RUs will be assigned with low access delay, and the utilization of RUs will be guaranteed. The simulation results show that the proposed adaptive allocation scheme outperforms the fixed allocation uplink OFDMA scheme in terms of throughput and access latency.