White matter lesions detected on magnetic resonance imaging scans of the brain have been hypothesized to have associations with the causes of several diseases. Accurate quantification of white matter lesions is important for the hypothesis validation. However, the clinical quantification is highly variable due to subjective opinions of different raters and is likely to compromise the reliability of the assessment. This paper introduces a new method of two-dimensional fuzzy weighted recurrence networks that can numerically express the quantity of white matter lesions. The results illustrate the promising application of the proposed method that offers as a useful computational tool in brain research.