In 1973, R. C. Entringer posed the problem of determining all graphs which are \emph{uniquely pancyclic}(see J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, New York,1976), p.247, Problem 10). The progress of all 50 problems in [J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, New York,1976)] can be find in Stephen C. Locke, Unsolved problems: http://math.fau.edu/locke/Unsolved.htm. In 1986, Y. Shi determined all uniquely pancyclic graphs of order $n$ with $n+m$ edges for $m\leq 3$ and conjectured that there are no other uniquely pancyclic graphs (see Y. Shi. Some theorems of uniquely pancyclic graphs. Discrete Math, 1986, 59: 167-180). A graph $G$ of order $n$ is said to be $r$-$(k)$-pancyclic graphs if G contains exactly $k$ cycles of length $t$ for all $t$ satisfying $r\leq t \leq n$ . In 2013, C. T. Zamfirescu constructed an infinite family of $r$-$(2)$-pancyclic graphs(see C. T. Zamfirescu.$(2)$- pancyclic graphs. Discrete Appl. Math,2013, 161: 1128-1136). In 2018, S. Liu constructed several infinite families of $r$-$(k)$-pancyclic graphs (see S. Liu. On $r$-$(k)$-pancyclic graphs[J]. Ars Combin, 2018, 140: 277-291). A graph $G$ of order $n$ is said to be $r$-$(d_{1},d_{2},\cdots,d_{t-1})$-pancyclic graphs if G contains exactly $d_{i}$ $(0\leq i\leq t-1)$ cycles of length $r+tj+i$ for all $r+tj+i$ satisfying $r+tj+i\leq n$ and $j$ is the number of $d_{1}$,$d_{2}$,$\cdots$,$d_{t-1}$ repeats. In this paper, we construct several infinite families of $r$-$(d_{1},d_{2},\cdots,d_{t-1})$-pancyclic graphs.