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This paper utilizes modern statistical and machine learning methodology to predict the oscillation mode of interest in complex power engineering systems. The damping ratio of the electromechanical oscillation mode is formulated as a function of the power of the generators and loads as well as bus voltage magnitudes in the entire power system. The celebrated Lasso algorithm is implemented to solve this high-dimension modeling problem. By the nature of the L1 design, the Lasso algorithm can automatically render a sparse solution, and by eliminating redundant features, it provides desirable prediction power. The resultant model processes a simple structure, and it is easily interpretable. The precision of our sparse modeling framework is demonstrated in the context of an IEEE 50-Generator 145-Bus power network and an online learning framework for the power system oscillation mode prediction is also provided.