The present study introduces a new scanning capillary tube viscometer for measuring fluid viscosity continuously over a range of shear rates including a low shear regime. Using a charge-coupled device sensor array, one could measure the changes in fluid level in a rising tube h(t) from which viscosity and shear rate were mathematically calculated. The concept of the new scanning capillary tube viscometer was validated by measuring viscosities of Newtonian fluids and comparing the results with those obtained with reference data and a rotating viscometer. Furthermore, the present method overcomes one of the major drawbacks of the capillary tube viscometer, the inability to produce viscosity data in a low shear range, by extending the shear rate range as low as 5 s−1 for water and diluted glycerin solutions at room temperature.