Problem statement: Technology Acceptance Model (TAM) is one of models that analyze user behavior to accept and use a new technology. SEM is the most statistical method which use in TAM analysis that provides the estimation strength of all hypothesized relationship between variables in a theoretical model. Consider to employing the standard SEM in TAM analysis which expected large data, the sample size become a crucial problem. Population census data processing is Indonesian government statistical program that needs supporting a computer technology in order to obtain accurate data and less time processing. It is needed to understand the user acceptance in mandatory environment with limited users. Approach: Estimation SEM with Bayesian method is an alternative to solve the sample size problem. This study the developing TAM in the implementation of census data processing system with limitation of sample size and extension of statistical methods of TAM’s analysis with Structural Equation Model (SEM) Bayesian approach. The TAM theory of this study implemented the constructs of TAM3: subjective norm, output quality, result demonstrability, perception of external control, compatibility and experience, perceived ease of use, perceived of usefulness. The others constructs are organizational interventions: management support, design characteristic, training, organizational support. Results: The result have shown that from the model there are significant relations between first: management support to subjective norm, second: subjective norm to perceived of usefulness, third: training, perception of external control to perceived ease of use. Residual analysis show that residuals are close to zero. Conclusion: Estimation of TAM using SEM and Bayesian methods with MCMC and Gibbs Sampler algorithm could handle the small sample size problem.