Using e + e − collision data samples with center-of-mass energies ranging from 2.000 to 2.644 GeV, collected by the BESIII detector at the BEPCII collider, and with a total integrated luminosity of 300 pb −1 , a partial-wave analysis is performed for the process e + e − → K + K − π 0 π 0 . The total Born cross sections for the process e + e − → K + K − π 0 π 0 , as well as the Born cross sections for the subprocesses e + e − → φπ 0 π 0 , K + (1460)K − , K + 1 (1400)K − , K + 1 (1270)K − and K * + (892)K * − (892), are measured versus the center-of-mass energy. The corresponding results for e + e − → K + K − π 0 π 0 and φπ 0 π 0 are consistent with those of BaBar and have much improved precision. By analyzing the cross sections for the four subprocesses, K + (1460)K − , K + 1 (1400)K − , K + 1 (1270)K − and K * + (892)K * − (892), a structure with mass M = (2126.5 ± 16.8 ± 12.4) MeV/c 2 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 − → K + 1 (1270)K − and 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).