We introduce a modified Poisson sampling, with a fixed lower bound of sample size. The design is a combination of simple random sampling and Poisson sampling. Simple random sampling is used to compensate for the lack of sample size from remaining elements in the finite population, after execution of a Poisson sampling. At the first stage, the units are sampled independently with given inclusion probabilities. But in the second stage, inclusion probabilities are dependent to each other. Because it is important to know, which of the elements are selected in the first stage and which of them are remained. Some advantages of our design are: simple performance, controlling sample size, ability to perform the method of probability proportional to size. The simulations show that the design can dominate its rival design in probability proportional to size sampling.