Based on the Stirling triangle of the second kind, the Whitney triangle of the second kind and one triangle of Riordan, we study a Stirling–Whitney–Riordan triangle $$[T_{n,k}]_{n,k}$$ satisfying the recurrence relation: $$\begin{aligned} T_{n,k}= & {} (b_1k+b_2)T_{n-1,k-1}+[(2\lambda b_1+a_1)k+a_2+\lambda ( b_1+b_2)] T_{n-1,k}+\\&\lambda (a_1+\lambda b_1)(k+1)T_{n-1,k+1}, \end{aligned}$$ where initial conditions $$T_{n,k}=0$$ unless $$0\le k\le n$$ and $$T_{0,0}=1$$ . We prove that the Stirling–Whitney–Riordan triangle $$[T_{n,k}]_{n,k}$$ is $$\mathbf{x} $$ -totally positive with $$\mathbf{x} =(a_1,a_2,b_1,b_2,\lambda )$$ . We show that the row-generating function $$T_n(q)$$ has only real zeros and the Turan-type polynomial $$T_{n+1}(q)T_{n-1}(q)-T^2_n(q)$$ is stable. We also present explicit formulae for $$T_{n,k}$$ and the exponential generating function of $$T_n(q)$$ and give a Jacobi continued fraction expansion for the ordinary generating function of $$T_n(q)$$ . Furthermore, we get the $$\mathbf{x} $$ -Stieltjes moment property and 3- $$\mathbf{x} $$ -log-convexity of $$T_n(q)$$ and show that the triangular convolution $$z_n=\sum _{i=0}^nT_{n,i}x_iy_{n-i}$$ preserves Stieltjes moment property of sequences. Finally, for the first column $$(T_{n,0})_{n\ge 0}$$ , we derive some properties similar to those of $$(T_n(q))_{n\ge 0}.$$