This paper presents a new approximation formula for pricing multi-dimensional discretely monitored average options and spread options in a local-stochastic volatility (LSV) model with jumps by applying an asymptotic expansion technique. Particularly, our model includes local-volatility functions and jump components in both the underlying asset price and its volatility processes. To the best of our knowledge, the proposed approximation is the first one which achieves analytic approximations for the average option prices in this environment.In numerical experiments, by employing several models we provide approximate prices for average and calendar spread options on the WTI futures based on the parameters through calibration to the listed (plain-vanilla) futures option prices, and compare those with the CME settlement prices, which confirms the validity of the method.Moreover, we show the LSV with jumps model is able to replicate consistently and precisely listed futures option, calendar spread option and average option prices with common parameters.