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In this paper, we will establish many explicit relations between parametricAp\'{e}ry-type series involving one or two parametric binomial coefficients andHurwitz-type multiple zeta values (with $r$-variables) by using the method ofiterated integral. Furthermore, we also establish some new identities ofintegrals involving multiple polylogarithm functions and Kaneko--Tsumura {\rmA}-functions in terms of Hurwitz-type multiple zeta values. Then, using theseformulas obtained, we obtain the explicit formulas of Arakawa-Kaneko zetavalues and Kaneko-Tsumura $\psi$-values. Moreover, we can find a symmetricformula of Kaneko-Tsumura's conjecture about double $T$-values. Finally, wedefine and discuss the Hurwitz-type multiple zeta values of parametric binomialcoefficient.

Parametric Ap\'{e}ry-type Series and Hurwitz-type Multiple Zeta Values