Alginate nanofibers have been attractive for potential tissue regeneration applications due to a combination of their moisture retention ability and large surface area available in a nonwoven nanofiber form. This study aims to address several challenges in alginate nanofiber application, including the lack of structural stability in aqueous environment and limited cell attachment as compared to commercial wound dressings, via examining crosslinking techniques. In addition to the commonly performed divalent ion crosslinking, a glutaraldehyde double-crosslinking step and polylysine addition were applied to an electrospun alginate nanofiber nonwoven mat. With optimization of the electrospinning solution, nanofiber morphology was maintained after the two-stage crosslinking process. Extensibility of the nanofiber mat reduced after the crosslinking process. However, both aqueous stability and cell attachment improved after the postspinning modifications, as shown through degradation tests in phosphate buffered saline solutions and fibroblast cell culture studies, respectively.