Liquid-core fibers, which are hollow core fibers or capillaries filled with liquids as core materials, have been attractively explored for various applications, especially in nonlinear optofluidics. High nonlinear refractive indices of selected liquids enable broadband supercontinuum generation. Unlike solid glasses, the nonlinear properties of liquids are more complex, including a contribution of electro-bound (instantaneous) nonlinearity and molecular rotation and vibration under external laser pulses (i.e., noninstantaneous nonlinearity). While the role of noninstantaneous nonlinearity in pulse evolution under anomalous dispersion has been extensively studied, its effect on pulse broadening in normal dispersion regimes remains unexplored. In this work, we numerically simulate pulse evolution in a liquid-core fiber with normal dispersion and high noninstantaneous nonlinearity. The results point out that this nonlinearity leads to narrow bandwidth and asymmetry spectrum of self-phase modulation and enhances simulated Raman scattering even at a low input power. High nonlinearity of the liquid provides an octave spanning supercontinuum generation (e.g., 1050-2700 nm with 1 kW input peak power and 20 ps input pulse-width); however, noninstantaneous nonlinearity significantly decreases the coherence through simulated Raman scattering. These results are valuable for understanding light-liquid interactions, not only for supercontinuum generation but also for applications in optofluidic lasers and sensors.