In this note, we attempt to use the Burr-type distributions to describe the software fault-detection time distribution, and develop somewhat different non-homogeneous Poisson process (NHPP)-based software reliability models (SRMs). From the viewpoints of the goodness-of-fit and predictive performances, we compare Burr-type NHPP-based SRMs with the existing ones having the well-known fault-detection time distributions. Throughout numerical examples with 16 software fault count data (8 time data and 8 group data) observed in actual software development projects, we show the usefulness of the Burr-type NHPP-based SRMs.