One of the challenging tasks in the field of pattern recognition is the recognition of handwritten characters. Handwritten characters are difficult to recognize as compared to printed characters because of large number of variations in writing style. This paper aims to find an efficient system for recognition of Odia handwritten numerals by using PSOFLANN (Particle Swarm Optimized Functional Link Artificial Neural Network) model. All basic steps of character recognition: preprocessing, feature extraction and classification are carried out to achieve the goal. In the preprocessing phase the numeric characters are normalized. In feature extraction phase gradient based approach is used for extraction of features. The extracted features are further reduced by using PCA (Principal Component Analysis). The generated features are then applied to PSOFLANN model for classification. In classification phase two approaches PSO (particle Swarm Optimization) and FLANN (Functional Link Artificial Neural Network) are combined to optimize the weights of FLANN for an efficient recognition system. The system is applied on the standard dataset collected from ISI Calcutta which consists of 1000 samples of Odia handwritten numerals ranging from 0-9. The proposed system achieved 89% accuracy on test dataset which shows the effectiveness of PSOFLANN model for recognition of handwritten Odia numerals.