In this paper, we investigate a new type of generalized derivations associated with Hochschild 2-cocycles which is introduced by A.Nakajima (Turk.\ J.\ Math.\ 30 (2006), 403--411). We show that if $\mathcal U$ is a triangular algebra, then every generalized Jordan derivation of above type from $\mathcal U$ into itself is a generalized derivation.