Ultrashort pulses (USPs) at wavelengths down to the communication window with a high repetition frequency range (GHz-THz) have found wide applications, especially, in bio- photonic sensors, optical coherence tomography, materials processing, etc.. There are some de- sirable features that USPs need to satisfy such as being pedestal-free and transform-limited for their suitability in communication as well as non-communication based applications. However, it is very difficult to meet out these desirable characteristicseven with carefully configured laser sys- tem. Hence, pulse-compression techniques have been the ultimate solution for generating USPs, in recent times. Having realized the importance of generating USPs through pulse compression, we aim at design- ing a novel practicable pulse compressor using a tapered photonic crystal fiber (PCF) operating down to ultraviolet regime. The pulse propagation in a tapered PCF is governed by the nonlinear Schrdinger (NLS) type equation. We adopt the self-similar scaling analysis for generating USPs. Based on the analytical results, we model a tapered PCF such that the dispersion decreases ex- ponentially while the nonlinearity increases exponentially along the propagation direction. Here, the required tapering is achieved by exponentially decreasing the diameter of the air hole as well as its pitch. We envisage that the proposed pulse compressor would turn out to be an excellent tool for generating high quality USPs down to ultraviolet regime, which, in turn, might be very much useful in bio-photonic related applications.