We introduce a simple volume conserving stochastic model undergoing a nonequilibrium roughening transition (NRT) in 1+1 dimensions. In our model, there is no deposition and evaporation of a particle breaking the volume conserving condition. The degree of roughness of the fluctuating interface in our model is determined by whether or not the hopping of a particle depends on the local slope of the interface. The hopping process of a particle is controlled by the probability 0<~p<~1. For p<1/2, a moving particle tends to hop in the downhill direction of the local slope of the interface, and so the interface is in a smooth phase with a zero roughness exponent. For p>1/2, a particle tends to hop in the uphill direction, and so the interface cannot reach a saturated phase. When p=1/2, the hopping of a particle does not depend on the local slope of the interface. Then the interface can reach a saturated phase. The saturated interface at p=1/2 is in a rough phase with a nonzero roughness exponent. Our model, therefore, exhibits the NRT at the critical parameter pc=1/2.