We present a study Of Viscous fingering patterns which arise because of the instability at the interface of two fluids of dissimilar viscosities. Viscous fingering experiments were performed in a lifting Hele-Shaw cell with a Newtonian defending fluid, castor oil or olive oil, while the invading fluid is air. We focus here on the fractal dimension of the patterns and how it varies with the lifting pressure in the Hele-Shaw cell. The fractal dimension of the fluid-air interface is measured by the divider step method. It is seen that the dimension changes from a value close to one, indicating no instability, to a value around 1.6 as the pressure is increased. A change in fractal dimension with time is also observed as the pattern evolves. Measurement of the fractal dimension offers a method for quantifying the instability.