Microflow cytometry is a powerful technique for characterization of particles suspended in a solution. In this work, we present a microflow cytometer based on viscoelastic focusing. 3D single-line focusing of microparticles was achieved in a straight capillary using viscoelastic focusing which alleviated the need for sheath flow or any other actuation mechanism. Optical detection was performed by fiber coupled light source and photodetectors. Using this system, we present the detection of microparticles suspended in three different viscoelastic solutions. The rheological properties of the solutions were measured and used to assess the focusing performance both analytically and numerically. The results were verified experimentally, and it has been shown that polyethlyene oxide (PEO) and hyaluronic acid (HA) based sheathless microflow cytometer demonstrates similar performance to state-of-the art flow cytometers. The sheathless microflow cytometer was shown to present 780 particles/s throughput and 5.8% CV for the forward scatter signal for HA-based focusing. The presented system is composed of a single capillary to accommodate the fluid and optical fibers to couple the light to the fluid of interest. Thanks to its simplicity, the system has the potential to widen the applicability of microflow cytometers.