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The future query of moving objects involves predicting their future positions based on their current locations and velocities to determine whether they will appear in a specified area. This technique is crucial for positioning and navigation, and its importance in our daily lives has become increasingly evident in recent years. Nonetheless, the growing volume of data renders traditional index structures for moving objects, such as the time-parameterized R-tree (TPR-tree), inefficient due to their substantial storage overhead and high query costs. Recent advancements in learned indexes have demonstrated a capacity to significantly reduce storage overhead and enhance query efficiency. However, most existing research primarily addresses static data, leaving a gap in the context of future queries for moving objects. We propose a novel <b>f</b>uture q<b>u</b>e<b>r</b>y technique for <b>m</b>oving <b>o</b>bjects based on a <b>l</b>earned <b>i</b>ndex (<b>FurMoLi</b> for short). FurMoLi encompasses four key stages: firstly, a data partition through clustering based on velocity and position information; secondly, a dimensionality reduction mapping two-dimensional data to one dimension; thirdly, the construction of a learned index utilizing piecewise regression functions; and finally, the execution of a future range query and future KNN query leveraging the established learned index. The experimental results demonstrate that FurMoLi requires 4 orders of magnitude less storage overhead than TPR-tree and 5 orders of magnitude less than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>B</mi><mo>+</mo></msup></semantics></math></inline-formula>-tree for moving objects (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>B</mi><mi>x</mi></msup></semantics></math></inline-formula>-tree). Additionally, the future range query time is reduced to just 41.6% of that for TPR-tree and 34.7% of that for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>B</mi><mi>x</mi></msup></semantics></math></inline-formula>-tree. For future KNN queries, FurMoLi’s query time is only 70.1% of that for TPR-tree and 47.4% of that for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>B</mi><mi>x</mi></msup></semantics></math></inline-formula>-tree.