  In this paper, we study how to construct f(R) gravity models. Cosmological
observations and local gravity tests imply that a viable f(R) model should be
very close to the LCDM model. We create procedures to construct viable
LCDM-like f(R) models, and present multiple models of three types. The
connections between some of these models are discussed. We also study the
cosmological evolution of the LCDM-like f(R) gravity. Exact numerical
integration can generate accurate cosmological evolution, but the numerical
simulation in the early-universe stage is slow due to the oscillations of the
field phi(= f') near the minimum of the effective potential. To avoid this
problem, we take the minimum of the effective potential as an approximate
solution for phi, and obtain the cosmological evolution. This approximate
method describes the cosmological evolution well except in the late universe.
Therefore, we use the approximate method in the early-universe evolution, and
use the exact method in the late-universe one.
