In order to verify the feasibility of expansion of back-fire limit equivalence ratio in the hydrogen-fueled engine with external mixture, the characteristics of performance and combustion are experimentally analyzed with change of intake/exhaust valve timings under the fixed valve overlap period of $0^{circ}$ CA(non-valve overlap period). These characteristics are also tested for the change of exhaust valve closing timing while intake valve opening timing is fixed to clear the main cause of back-fire occurrence. As the results, the less valve overlap period center is retarded, the more back-fire limit equivalence ratio increases and back-fire does not occurred after TDC. In addition, it was shown that the control of back-fire is dependent on intake valve opening timing than valve overlap period.