To broaden the application scenario and reduce energy consumption, we propose an energy-efficient fixed-gain (FG) amplify-and-forward (AF) relay assisted orthogonal frequency-division multiplexing with index modulation (OFDM-IM) scheme in this letter. The proposed system needs neither instantaneous channel state information (CSI) nor complicated processing at the relay node. It operates based on the power allocation scheme that minimizes the sum of transmit power at both source and relay node, given an outage probability constraint. Through a series of problem transformation and simplification, we convert the original power allocation problem to its relaxed version and solve it using convex programming techniques. To reveal the computing efficiency of the proposed power allocation scheme, we analyze its computational complexity. Numerical simulations substantiate that the proposed optimization scheme has a neglectable loss compared with the brute force search, but the computational complexity can be considerably reduced.