Conduction-cooled superconducting magnets are cooled by cryocooler alone through the conductive thermal links. The limited refrigeration capacity and conductive cooling make the magnets more prone to quench. We have studied the quench characteristics of a 6 T conduction-cooled NbTi magnet system in detail in this paper. The NbTi magnet has been designed for 102 A with 31% current margin to achieve 0.8 K temperature margin. During a training quench at 101.2 A, the outer surface of the NbTi magnet reached 53.25 K and the temperature of the 2nd stage cold head of the cryocooler reached 15.8 K. Conductive cooling by the cryocooler makes the post-quench recovery of the NbTi magnet in 40 minutes. The maximum sweep rate is 6 A/min for thermally stable operation of this conduction-cooled NbTi magnet. We have done an intentional quench at a sweep rate of 8 A/min. The maximum hot-spot temperature and the post-quench current decay have been simulated using a finite element analysis (FEA) code. Post-quench distribution of the dumped energy in the different components of the magnet system is also presented.