A memory access control apparatus includes a plurality of memory access request generating modules and an arbitrator. When one of the memory access request generating modules receives a second memory access event while a memory device is performing a first memory access operation according to a first memory access request in response to a first memory access event, the memory access request generating module outputs a second memory access request corresponding to the second memory access event to the memory device after a delay time. The arbitrator is implemented for arbitrating memory access requests respectively outputted from the memory accessing request generating modules.