Highly coherent visible supercontinuum (SC) sources are demanded for many applications such as bio-sensing and imaging. Either dispersion management on the fiber or optimizing ultrafast pulsed pump parameters can work for achieving broadband coherent fiber SC. Normally, highly coherent SC with medium bandwidth can be obtained in an all-normal-dispersion (ANDi) nonlinear photonic crystal fiber (PCF), which has normal dispersion for all the wavelengths by tailoring the structure parameters of the microstructured cladding to sub-wavelength scale. Hence, such an ANDi fiber requires a submicron core diameter, and it makes precise fabrication challenging. Instead, using a standard anomalous dispersion pumping scheme and an ultrafast pulsed pump source, broadband SC with a high degree of coherence can also be obtained. In this study, we report broadband visible SC with a high degree of coherence approaching unity in a low-index borosilicate glass air-suspended PCF with a micrometer-core diameter, by the anomalous dispersion pumping scheme. The pulse duration of the 800 nm Ti:sapphire femtosecond laser is 29 fs. The experimental results are in good agreement with the numerical simulations, indicating that ultrashort pump pulses are the primary cause for the high degree of the generated visible SC, while the weak Raman effect of the borosilicate glass host plays a non-negligible but secondary role in the procedure of coherent SC generation.