The present disclosure provides a concrete structure strengthened using a grid reinforcement material and non-shrink grout and a method of strengthening the same in which, when strengthening a concrete structure such as a concrete slab or a concrete wall body that is damaged or deteriorated, a grid reinforcement material is mounted on one side of the concrete structure, a formwork is formed on an outer side of the grid reinforcement material to have a required gap, and then the gap is filled with non-shrink grout so that the non-shrink grout is cured therein to strengthen the old concrete structure, thereby being able to automatically fill and repair cracks formed in the concrete structure just by injecting the non-shrink grout without separately performing crack repair on the old concrete structure. Also, the grid reinforcement material may be easily fixed or mounted using a grid fixing device and may be easily applied to strengthening of a concrete structure having a curved surface as well as a concrete structure having a flat surface such as a concrete slab or a concrete wall body. In addition, reinforcing bars may be additionally arranged in a gap between a surface of the concrete structure and the grid reinforcement material so that the grid reinforcement material increases a cover thickness, and thus the concrete structure is remarkably strengthened.