A modified BDS Klobuchar ionospheric time-delay correction model (MBDK) is proposed for single-frequency users of the BeiDou Navigation Satellite System (BDS). Instead of using a constant night-time delay (5 ns) in the broadcast BDS Klobuchar model (BDSK), the night-time delay is considered a parameter and estimated hourly in our new model. To keep the same number of eight ionospheric coefficients transmitted in the navigation message, the fourth legacy coefficient of the period term is replaced by the new night-time parameter. The fitted legacy BDS Klobuchar model (BDFK) that is re-estimated using the same input ionospheric total electron content (TEC) data for the MBDK is also included for comparison. Tests from day of year 155 to 366 in 2020 demonstrate that the proposed MBDK model performs better than the broadcast BDSK model and the fitted BDFK model in comparison with the global ionospheric maps provided by the International GNSS Service (IGS). The root mean square values of the BDSK and BDFK are 5.2 and 4.3 TEC unit (TECU), respectively, while it is 3.7 TECU for the MBDK, showing improvements of 29% and 14%, respectively, on the global scale. When only considering the northern hemisphere, the improvements are increased significantly to 47% and 33%, mainly because of the use of only northern hemisphere ionospheric data for the generation of the MBDK model. In the northern hemisphere, the BDSK, BDFK and MBDK models can correct 64%, 71% and 78% of the ionospheric time delay, respectively. Twenty IGS stations are selected to analyze the positioning error induced by the residual ionospheric delay after using the MBDK. The average ionospheric errors of the BDSK, BDFK and MBDK are 5.1, 4.4 and 3.9 TECU, respectively. As expected, the MBDK exhibits the best performance, which outperforms the BDSK and BDFK by 22% and 11%, respectively. It should be mentioned that the performance of the BDSK, BDFK and MBDK in the southern hemisphere is worse than that in the northern hemisphere due to the simple "symmetrical strategy" used. We recommend adding ionospheric input data in the southern hemisphere to improve the precision of the BDS Klobuchar model in this hemisphere.