Iterative Stencil Loops (ISLs) are the key kernel within a range of compute-intensive applications. To accelerate ISLs with Field Programmable Gate Arrays, it is critical to exploit parallelism (1) among elements within the same iteration and (2) across loop iterations. We propose a novel ISL acceleration scheme called Direct Computation of Multiple Iterations (DCMI) that improves upon prior work by pre-computing the effective stencil coefficients after a number of iterations at design time—resulting in accelerators that use minimal on-chip memory and avoid redundant computation. This enables DCMI to improve throughput by up to 7.7× compared to the state-of-the-art cone-based architecture.