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Let $X$ be a normal projective variety with only klt singularities, and $L_X$a strictly nef $\mathbb{Q}$-divisor on $X$. In this paper, we study thesingular version of Serrano's conjecture, i.e., the ampleness of $K_X+t L_X$for sufficiently large $t\gg 1$. We show that, if $X$ is assumed to be a$\mathbb{Q}$-factorial Gorenstein terminal threefold, then $K_X+tL_X$ is amplefor $t\gg 1$ unless $X$ is a weak Calabi-Yau variety (i.e., the canonicaldivisor $K_X\sim_\mathbb{Q}0$ and the augmented irregularity $q^\circ(X)=0$)with $L_X\cdot c_2(X)=0$.

Strictly nef divisors on singular threefolds