Ruin problems in the ordinary renewal risk model with stochastic investment were examined. The asset price process of investment is denoted by $\{e^{R_t},\ t\geqslant 0\}$, where $R_t$ is assumed to be a L\'{e}vy process. By constructing a supermartingale associated with the ruin time of the surplus process with investment, an upper bound for ultimate ruin probability bymartingale approach was presented. The impact of inter-arrival times of claims on ruin probability was considered by numerical method.