The filtering of irregularly sampled bandlimited functions is discussed in this letter. An algorithm is given that enables the filtering of bandlimited functions with bandlimited filters to a desired precision, provided some requirements on the sampling density are met. All operations are carried out on the irregular samples themselves. The resulting algorithm is iterative in nature and converges quickly. It is also computationally tractable as it only requires matrix-vector multiplications. The algorithm is noncausal irrespective of the precise characteristics of the filter used, i.e., a buffer is necessary for implementation. The algorithm is evaluated on synthetic examples for which ground truth functions can be derived analytically.