The first principles density functional theory (DFT) approach (GGA-PW91/DNP) was used to study the addition reaction of methylamine to fullerenes C-50 and C-60 or single-walled carbon nanotubes (SWNTs) (5,5) and (10,0). To understand the relationship between reactivity and curvature, various addition sites have been investigated for comparisons. The DFT calculation results showed that the reaction energy of the addition of methylamine onto C-60 or the closed caps of (5,5) and (10,0) is rather low. Moreover, the reaction at a few sites even appears exothermic. However, the reaction on the perfect sidewall of the nanotubes is always endothermic, and the reaction energy is much higher than that on the caps. The energetically preferable addition sites are the carbon atoms located at the vertexes formed with five-, five-, six-membered rings on C-50 or five-, five-, seven-membered rings on defects of nanotubes. The systematic theoretical study revealed that the pyramidalization and pi-orbital misalignment could result in an increased reactivity of these pentagon-pentagon fusion sites. The reactivity depends on the pyramidalization angle, which is a quantitative measurement of the local curvature and strain of the reaction center.