"We are working with them in the same manner we worked with the JetBlue (JBLU) organizing committee," Moak said in an interview. "We are confident we will have a positive outcome."
JetBlue pilots voted to join ALPA in April, with 71% of voters backing the union. Two earlier organizing campaigns failed.
"The win shows the strong desire of JetBlue pilots to gain a meaningful voice in their future, the certainty of a collective bargaining agreement, and the resources needed to be relevant," ALPA said in a prepared statement following the April election. "These objectives motivated the overwhelming grass roots effort by JetBlue pilots which led to today's vote."
A Virgin America spokeswoman declined to comment on Wednesday.
In August, Virgin America flight attendants voted to join the Transport Workers Union after rejecting the same union in a 2011 vote. Of 737 flight attendants who voted, 58% backed the union.
Virgin America shares have been gaining ground rapidly since they began trading Friday following an initial public offering that raised $306 million. The offering price was $23 a share.
In mid-morning trading on Wednesday, shares were down 49 cents to $36.56.