In this paper, molecular quantum computation is numerically studied with the quantum search algorithm (Grover's algorithm) by means of optimal control simulation. Qubits are implemented in the vibronic states of I2, while gate operations are realized by optimally designed laser pulses. The methodological aspects of the simulation are discussed in detail. We show that the algorithm for solving a gate pulse-design problem has the same mathematical form as a state-to-state control problem in the density matrix formalism, which provides monotonically convergent algorithms as an alternative to the Krotov method. The sequential irradiation of separately designed gate pulses leads to the population distribution predicted by Grover's algorithm. The computational accuracy is reduced by the imperfect quality of the pulse design and by the electronic decoherence processes that are modeled by the non-Markovian master equation. However, as long as we focus on the population distribution of the vibronic qubits, we can search a target state with high probability without introducing error-correction processes during the computation. A generalized gate pulsedesign scheme to explicitly include decoherence effects is outlined, in which we propose a new objective functional together with its solution algorithm that guarantees monotonie convergence.