Fused Filament Fabrication (FFF), a most widely used additive manufacturing process in which a relatively rigid polymer filament feedstock is delivered through a liquefier by an extruder. Objects are built layer by layer using FFF, which is continuously developing to a technology that has a broader scope beyond simply modeling and prototyping. In FFF, polymer or polymer composite filament feedstock is processed in molten state, therefore understanding the polymer melt flow behavior is critical as it is needed to predict final product quality and to improve the processing performance. Rheology as a vital tool for analyzing the material flow has been applied FFF. Unfortunately, methods for assessing the melt flow rheology of an FFF polymer or polymer composite filament are lacking. To address this need, our research develops a low-cost device capable of estimating the shear rate dependent viscosity directly from the filament feedstock. In our approach, the force required to process polymer filament through a heated nozzle typical of today’s desktop FFF machines is measured. To gain a complete understanding of the melt flow behavior, math models are presented which relates the pressure drop of the complex flow to flow rate, making it possible to estimate Power Law and Carreau-Yasuda model parameters. Experiments are performed to evaluate model parameters for neat ABS of two brands, carbon fiber filled ABS, Amphora, and carbon fiber filled PLA over a temperature range of 200°C to 230°C using our device. Initial results show that we can accurately predict the Power Law index for these materials as compared to results obtained using a HAAKE MARS 40 rotational rheometer. The comparison of the resulting data indicates that the Cox-Mertz rule is valid for low fiber concentration (< 15%) reinforced polymer composites. Our results show that our device provides a way to measure the rheological property of polymer or polymer composite used specifically in FFF.