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The rapid growth of GPS technology and mobile devices has led to a massive accumulation of location data, bringing considerable benefits to individuals and society. One of the major usages of such data is travel time prediction, a typical service provided by GPS navigation devices and apps. Meanwhile, the constant collection and analysis of the individual location data also pose unprecedented privacy threats. We leverage the notion of geo-indistinguishability, an extension of differential privacy to the location privacy setting, and propose a procedure for privacy-preserving travel time prediction without collecting actual individual GPS trace data. We propose new concepts to examine the impact of the geo-indistinguishability sanitization on the usefulness of GPS traces and provide analytical and experimental utility analysis for privacy-preserving travel time prediction. We also propose new metrics to measure the adversary error in learning individual GPS traces from the collected sanitized data. Our experiment results suggest that the proposed procedure provides travel time analysis with satisfactory accuracy at reasonably small privacy costs.