Was he insecure or unsure that God who performed miracle through him, would also save him from Jezebel?
We aren't told explicitly of course, but we do know that he was afraid Jezebel would kill him:
2Then Jezebel sent a messenger to Elijah, saying, “So may the gods do to me and more also, if I do not make your life as the life of one of them by this time tomorrow.” 3Then he was afraid, and he arose and ran for his life and came to Beersheba, which belongs to Judah, and left his servant there.ESV
But he was apparently not afraid of death itself:
4But he himself went a day's journey into the wilderness and came and sat down under a broom tree. And he asked that he might die, saying, “It is enough; now, O Lord, take away my life, for I am no better than my fathers.”ESV
Elijah seems to have had great confidence that God will judge the Baal-worshipers, but very little confidence that God would not also allow all his prophets to be killed by the sword:
10He said, “I have been very jealous for the Lord, the God of hosts. For the people of Israel have forsaken your covenant, thrown down your altars, and killed your prophets with the sword, and I, even I only, am left, and they seek my life, to take it away.”ESV
And God answers Elijah by promising that though yet more evil will afflict Israel, all those who remain faithful will escape:
18Yet I will leave seven thousand in Israel, all the knees that have not bowed to Baal, and every mouth that has not kissed him.”ESV
Assuming this speaks to the fear Elijah had, we can reason that Elijah was despairing that God's judgement would allow none to escape—indeed Paul quotes this verse in Romans 11 to support his argument that God has not utterly rejected his people Israel:
1I ask, then, has God rejected his people? By no means! For I myself am an Israelite, a descendant of Abraham, a member of the tribe of Benjamin. 2God has not rejected his people whom he foreknew. Do you not know what the Scripture says of Elijah, how he appeals to God against Israel? 3“Lord, they have killed your prophets, they have demolished your altars, and I alone am left, and they seek my life.” 4But what is God's reply to him? “I have kept for myself seven thousand men who have not bowed the knee to Baal.” 5So too at the present time there is a remnant, chosen by grace. 6But if it is by grace, it is no longer on the basis of works; otherwise grace would no longer be grace.ESV
Elijah's fear that God would not save Israel and would destroy all without mercy was perhaps more rational than fearing that God could not save him from Jezabel (as your question asks if I understand it correctly)—though perhaps he should have know better and been confident that God would always preserve a portion of Israel as His inheritance. But then again, Elijah was a man with a nature like ours, so perhaps it is not surprising that he did not.