We applied the method of conditional least squares for estimating parameters of NUAR(1). This process can be represented as the random coefficient autoregressive time series of the form $$ X_n=U_n X_{n-1}+V_n, $$ where $\{(U_n,V_n)\}$ is the sequence of independent identically distributed random vectors such that supply the elements of the sequence $\{X_n\}$ with $\mathcal{U}(0,1)$ marginal distribution. Defined estimates were the functions of the estimates of moments $E(U_n)$ and $E(U_n V_n)$ and they are strong consistent and asymptotically normally distributed.