Flavodoxin (Fld) has been demonstrated to bind to ferredoxin-NADP$^+$ reductase A (FprA) in Pseudomonas putida. Two residues ($Phe^{256}$, $Lys^{259}$) of FprA are likely to be important for interacting with Fld based on homology modeling. Site-directed mutagenesis and pH-dependent enzyme kinetics were performed to further examine the role of these residues. The catalytic efficiencies of FprA-$Ala^{259}$ and FprA-$Asp^{259}$ proteins were two-fold lower than those of the wild-type FprA. Homology modeling also strongly suggested that these two residues are important for electron transfer. Thermodynamic properties such as entropy, enthalpy, and heat capacity changes of FprA-$Ala^{259}$ and FprA-$Asp^{259}$ were examined by isothermal titration calorimetry. We demonstrated, for the first time, that $Phe^{256}$ and $Lys^{259}$ are critical residues for the interaction between FprA and Fld. Van der Waals interactions and hydrogen bonding were also more important than ionic interactions for forming the FprA-Fld complex.