The unpredictability degree and bandwidth properties of chaotic signals generated by semiconductor lasers subject to dual chaotic optical injections (DCOI) are investigated numerically. The unpredictability degree is evaluated quantitatively via permutation entropy. Compared with the slave laser (SL) subject to single chaotic optical injection, both the chaotic bandwidth and the unpredictability degree can be enhanced significantly for SL with DCOI. The effects of injection strength, frequency detuning as well as feedback strength are considered. It is shown that, with the increase of injection strength, the unpredictability degree of chaotic signals generated by SL increases firstly and then decreases until saturates at a constant level. Positive frequency detuning is preferred to achieve wideband unpredictability-enhanced chaos, and higher bandwidth and unpredictability degree can be further expected by adopting two differently detuned master lasers. The physical mechanisms behind the wideband unpredictability-enhanced chaos are also revealed. The wideband unpredictability-enhanced chaotic signals generated by SL with DCOI are extremely useful for high speed random number generators, as well as for high capacity security-enhanced chaotic communications.