The slime mould algorithm (SMA) is a recently developed meta-heuristic optimization algorithm which is based on the oscillation mode of slime mould in nature. However, the SMA is often trapped in local optima for global continuous optimization problems. To strengthen SMA's exploration for global optimum, we propose a modified SMA, which takes randomization based on a Levy distribution instead of the traditional uniform one, namely LF-SMA. Our LF-SMA is integrated with Levy-flight guidance to its optimal paths for connecting food with excellent exploratory propensity. Experimental results show that the proposed LF-SMA achieves better performance in 13 benchmark test functions and one investigated engineering case in terms of both computation cost and solution.