The calm markets of recent months have meant more trades are getting done in the dark.

Dark pools—private trading platforms, typically geared toward big investors—have enjoyed growing market share this year. The share of U.S. stock trades executed on dark pools and other off-exchange trading venues rose to 38.6% in April, the highest level in more than a year, according to research firm Tabb Group, and up from 34.7% in December.

When...