We investigate a modified Anderson model at the large-N limit,where the Coulomb interaction is replaced by the Sachdev-Ye-Kitaev random interaction.The resistivity of conduction electron ρc has a minimum value around temperature T*,which is similar to the Kondo system,but the impurity electron's density of state Ad(co)demonstrates no sharp-peak like the Kondo resonance around the Fermi surface.This provides a counterintuitive example where resistivity minimum exists without Kondo resonance.The impurity electron's entropy Sd and specific heat capacity Cv show a crossover from Fermi liquid to a non-Fermi liquid behavior dependent on temperature.The system is a Fermi liquid at T＜T*,and becomes a non-Fermi liquid at T＞T*,and then becomes a Fermi gas at sufficiently high temperatures T>>T*.The non-Fermi liquid at the intermediate-T regime does not occur in the standard Anderson model.We also make a renormalization group analysis,which confirms the crossover from Fermi liquid to the non-Fermi behavior.It is emphasized that the resistivity minimum emerges in our model when the system behaves as a non-Fermi liquid rather than Fermi liquid,which provides an alternative example showing resistivity minimum in condensed matter physics.