Let M β ( α ) [ α ≥ 0       and       β ≥ 0 ] denote the class of all functions f ( z ) = z + ∑ n = 2 ∞ a n z n analytic in the unit disc U with f ′ ( z ) f ( z ) / z ≠ 0 and which satisfy for z = r e i θ ∈ U the condition - \beta \pi \]" display="block"> ∫ θ 1 θ 2 Re { ( 1 − α ) z f ′ ( z ) f ( z ) + α ( 1 + z f ″ ( z ) f ′ ( z ) ) } d θ > − β π for all \theta _1 $"> θ 2 > θ 1 . In this note we show that each f ∈ M β ( α ) is close-to-star of order β when 0 < β ≤ α .