A partial-wave analysis is performed for the process e+e-→K+K-π0π0 at the center-of-mass energies ranging from 2.000 to 2.644 GeV. The data samples of e+e-collisions, collected by the BESIII detector at the BEPCII collider with a total integrated luminosity of 300 pb-1, are analyzed. The total Born cross sections for the process e+e-→K+K-π0π0, as well as the Born cross sections for the subprocesses e+e-→φπ0π0, K+(1460)K-, K1+(1400)K-, K1+(1270)K-, and K∗+(892)K∗-(892), are measured versus the center-of-mass energy. The corresponding results for e+e-→K+K-π0π0 and φπ0π0 are consistent with those of BABAR with better precision. By analyzing the cross sections for the four subprocesses, K+(1460)K-, K1+(1400)K-, K1+(1270)K-, and K∗+(892)K∗-(892), a structure with mass M=(2126.5±16.8±12.4) MeV/c2 and width Γ=(106.9±32.1±28.1) MeV is observed with an overall statistical significance of 6.3σ, although with very limited significance in the subprocesses e+e-→K1+(1270)K- A nd K∗+(892)K∗-(892). The resonant parameters of the observed structure suggest it can be identified with the φ(2170), thus the results provide valuable input to the internal nature of the φ(2170).