We present a theoretical investigation of enhanced supercontinuum (SC) generation in a lead silicate photonic crystal fiber with the aid of tan-hyperbolic Gaussian pulses of peak power of 100 W, pulse duration of 50 fs, and pumped at a 1550-nm wavelength. It is observed that the generated spectra are asymmetric and composed of oscillatory structures. The span of the spectra increases, extending more toward the longer wavelength region with the increase of the tan-hyperbolic factor Ω₀. The SC spectrum for Ω₀  =  1.50 is found to be about 1.4 times wider than its Gaussian counterpart. This work may have potential applications in photonic and optoelectronic devices.